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Paperpile-PhD.bib
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% Generated by Paperpile. Check out http://paperpile.com for more information.
% BibTeX export options can be customized via Settings -> BibTeX.
% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Higuchi1993-cd,
title = "Coexistence of infinite (*)-clusters {II}. Ising percolation in
two dimensions",
author = "Higuchi, Yasunari",
abstract = "SummaryWe show a strong type of conditionally mixing property
for the Gibbs states ofd-dimensional Ising model when the
temperature is above the critical one. By using this property,
we show that there is always coexistence of infinite (+ *)-and
(−*)-clusters when $\beta$ is smaller than $\beta$c andh=0 in
two dimensions. It is also possible to show that this
coexistence region extends to some non-zero external field case,
i.e., for every $\beta$ 0 such that |h|<hc($\beta$) implies the
coexistence of infinite (*)-clusters with respect to the Gibbs
state for ($\beta$,h).",
journal = "Probab. Theory Related Fields",
publisher = "Springer-Verlag",
volume = 97,
number = "1-2",
pages = "1--33",
month = mar,
year = 1993,
keywords = "Gumbel;PhD",
language = "en"
}
@ARTICLE{Sweeny1983-ci,
title = "Monte Carlo study of weighted percolation clusters relevant to
the Potts models",
author = "Sweeny, Mark",
journal = "Phys. Rev. B: Condens. Matter Mater. Phys.",
volume = 27,
number = 7,
pages = "4455",
year = 1983,
keywords = "PhD",
original_id = "313e1884-435b-0717-a8c1-917e107c515d"
}
@INCOLLECTION{LeVeque2007-pd,
title = "Chapter 7 - Absolute Stability for Ordinary Differential
Equations",
booktitle = "Finite Difference Methods for Ordinary and Partial
Differential Equations",
author = "LeVeque, Randall J",
volume = 2,
pages = "149--166",
year = 2007,
keywords = "PhD",
original_id = "3155c326-80bb-0d9e-8f45-0e16cdc4dbe4"
}
@BOOK{Thompson1972-sb,
title = "Mathematical statistical mechanics",
author = "Thompson, Colin John",
publisher = "Macmillan",
pages = "288",
year = 1972,
address = "New York, NY",
keywords = "PhD",
original_id = "72b77817-8be1-0462-b934-6b099b3f843a"
}
@BOOK{Lukacs1970-qm,
title = "Characteristic Functions",
author = "Lukacs, Eugene",
publisher = "Griffin",
pages = "1--360",
edition = "Second",
year = 1970,
address = "London",
keywords = "Probability; characteristic function;PhD",
original_id = "40963d96-f188-05dc-9cb5-8b4189474177"
}
@BOOK{Ellis2005-gd,
title = "Entropy, large deviations and statistical mechanics",
author = "Ellis, Richard",
publisher = "Springer-Verlag",
year = 2005,
address = "New York, NY",
keywords = "PhD",
original_id = "c9ba332b-f200-0226-a8fb-924b5ca9bf20"
}
@BOOK{Van_der_Vaart_undated-of,
title = "Weak Convergence and Empirical Processes with Applications to
Statistics",
author = "van der Vaart, Aad W and Wellner, Jon A",
publisher = "Springer",
series = "Springer Series in Statistics",
keywords = "PhD",
original_id = "36ef199b-897a-0a38-8b8d-44fe9706be3f"
}
@BOOK{Klebaner2005-jn,
title = "Introduction to Stochastic Calculus with Applications",
author = "Klebaner, Fima C",
publisher = "Imperial College Press",
edition = "Second Edi",
year = 2005,
address = "Singapore",
keywords = "PhD",
original_id = "5d251b67-0945-0350-9a19-660660dd5cd1"
}
@BOOK{Yushkevich_undated-wg,
title = "Mathematics of the 19th Century: Vol {II}",
author = "Yushkevich, A P and Kolmogorov, A N",
publisher = "Birkhauser",
keywords = "PhD",
original_id = "3df5b1ef-8fed-0c45-be69-1844af26da9f"
}
@BOOK{Bertsekas1995-mh,
title = "Nonlinear Programming",
author = "Bertsekas, Dimitri P",
publisher = "Athena Scientific",
year = 1995,
keywords = "PhD",
original_id = "cf15f3eb-d719-0709-9019-2fc76bfbf698"
}
@INCOLLECTION{LeVeque2007-sk,
title = "Chapter 9 - Diffusion Equations and Parabolic Problems",
booktitle = "Finite Difference Methods for Ordinary and Partial
Differential Equations",
author = "LeVeque, Randall J",
pages = "181--200",
year = 2007,
keywords = "PhD",
original_id = "fbf2c413-a357-02ca-bfa7-fdd768da3941"
}
@ARTICLE{Lindsay1983a-he,
title = "The Geometry of Mixture Likelihoods, Part {II}: The
Exponential Family",
author = "Lindsay, Bruce G",
abstract = "Project Euclid - mathematics and statistics online",
journal = "Ann Stat",
publisher = "Institute of Mathematical Statistics",
volume = 11,
number = 3,
pages = "783--792",
month = sep,
year = 1983,
keywords = "Mixture; maximum likelihood; curvature;Mixtures;PhD",
original_id = "43d5cead-9bc0-02a6-ad50-6a66bc4c9330"
}
@ARTICLE{Chiarini2016-xy,
title = "Extremes of Some Gaussian Random Interfaces",
author = "Chiarini, Alberto and Cipriani, Alessandra and Hazra, Rajat
Subhra",
journal = "J. Stat. Phys.",
volume = 165,
number = 3,
pages = "521--544",
series = "Stochastic interface models. Lectures on probability theory and
statistics",
month = nov,
year = 2016,
keywords = "Gumbel;PhD"
}
@BOOK{Liggett1985-ke,
title = "Interacting Particle Systems:",
author = "Liggett, Thomas M",
publisher = "Springer New York",
series = "Grundlehren der mathematischen Wissenschaften",
year = 1985,
keywords = "Gumbel;PhD"
}
@ARTICLE{Stefanski1990-uo,
title = "Deconvoluting kernel density estimators",
author = "Stefanski, Leonard A and Carroll, Raymond J",
abstract = "This paper considers estimation of a continuous bounded
probability density when observations from the density are
contaminated by additive measurement errors having a known
distribution. Properties of the estimator obtained by
deconvolving a kernel estimator of the observed data are
investigated. When the kernel used is sufficiently smooth the
deconvolved estimator is shown to be pointwise consistent and
bounds on its integrated mean squared error are derived. Very
weak assumptions are made on the measurement-error density
thereby permitting a comparison of the effects of different
types of measurement error on the deconvolved estimator",
journal = "Statistics",
publisher = "Taylor \& Francis",
volume = 21,
number = 2,
pages = "169--184",
month = jan,
year = 1990,
keywords = "Deconvolution;PhD"
}
@ARTICLE{Delaigle2007-ev,
title = "Frequent problems in calculating integrals and optimizing
objective functions: a case study in density deconvolution",
author = "Delaigle, A and Gijbels, I",
abstract = "Many statistical procedures involve calculation of integrals or
optimization (minimization or maximization) of some objective
function. In practical implementation of these, the user often
has to face specific problems such as seemingly numerical
instability of the integral calculation, choices of grid points,
appearance of several local minima or maxima, etc. In this paper
we provide insights into these problems (why and when are they
happening?), and give some guidelines of how to deal with them.
Such problems are not new, neither are the ways to deal with
them, but it is worthwhile to devote serious considerations to
them. For a transparant and clear discussion of these issues, we
focus on a particular statistical problem: nonparametric
estimation of a density from a sample that contains measurement
errors. The discussions and guidelines remain valid though in
other contexts. In the density deconvolution setting, a kernel
density estimator has been studied in detail in the literature.
The estimator is consistent and fully data-driven procedures
have been proposed. When implemented in practice however, the
estimator can turn out to be very inaccurate if no adequate
numerical procedures are used. We review the steps leading to
the calculation of the estimator and in selecting parameters of
the method, and discuss the various problems encountered in
doing so.",
journal = "Stat. Comput.",
publisher = "Springer US",
volume = 17,
number = 4,
pages = "349--355",
month = dec,
year = 2007,
keywords = "Deconvolution;PhD",
language = "en"
}
@ARTICLE{Delaigle2004-fy,
title = "Practical bandwidth selection in deconvolution kernel density
estimation",
author = "Delaigle, A and Gijbels, I",
abstract = "Kernel estimation of a density based on contaminated data is
considered and the important issue of how to choose the
bandwidth parameter in practice is discussed. Some plug-in (PI)
type of bandwidth selectors, which are based on non-parametric
estimation of an approximation of the mean integrated squared
error, are proposed. The selectors are a refinement of the
simple normal reference bandwidth selector, which is obtained by
parametrically estimating the approximated mean integrated
squared error by referring to a normal density. A simulation
study compares these PI bandwidth selectors with a bootstrap
(BT) and a cross-validated (CV) bandwidth selector. It is
concluded that in finite samples, an appropriately chosen PI
bandwidth selector and the BT bandwidth selector perform
comparably and both outperform the CV bandwidth. The use of the
various practical bandwidth selectors is illustrated on a real
data example.",
journal = "Comput. Stat. Data Anal.",
publisher = "Elsevier",
volume = 45,
number = 2,
pages = "249--267",
month = mar,
year = 2004,
keywords = "Bandwidth selection; Bootstrap; Cross-validation; Deconvolution;
Errors-in-variables; Kernel density estimation; Plug-in
methods;Deconvolution;PhD"
}
@BOOK{David2003-mk,
title = "Order Statistics",
author = "David, Herbert A and Nagaraja, H N",
publisher = "John Wiley \& Sons, Inc.",
month = jul,
year = 2003,
keywords = "PhD",
original_id = "4f012993-0ce8-0ece-baff-20ec8aae4092"
}
@INPROCEEDINGS{Hartigan1985-wn,
title = "A failure of likelihood asymptotics for normal mixtures",
booktitle = "Proceedings of the Berkeley conference in honor of Jerzy
Neyman and Jack Kiefer",
author = "Hartigan, J A",
volume = 2,
pages = "807--810",
institution = "Wadsworth, Belmont, CA",
year = 1985,
keywords = "PhD",
original_id = "fcb0580a-be32-08e2-9669-df68d811dd4c"
}
@BOOK{Barndorff-Nielsen2014-qk,
title = "Information and Exponential Families in Statistical Theory",
author = "Barndorff-Nielsen, O",
publisher = "Wiley",
series = "Wiley Series in Probability and Statistics",
year = 2014,
keywords = "PhD",
original_id = "f7a56444-9d8c-03ed-94eb-62828aecdd9c"
}
@BOOK{Rudin1987-bk,
title = "Real and complex analysis",
author = "Rudin, Walter",
year = 1987,
keywords = "PhD",
original_id = "5cd6986e-6b6b-083b-9ec7-2ec945913a4f"
}
@ARTICLE{Hall1999-tm,
title = "Density estimation under constraints",
author = "Hall, P and Presnell, B",
journal = "J. Comput. Graph. Stat.",
volume = 8,
number = 2,
pages = "259--277",
year = 1999,
keywords = "biased bootstrap; cressie; curve estimation; empirical;
entropy; kernel methods; likelihood; mode; read distance;
smoothing; weighted bootstrap;PhD",
original_id = "9f6f7443-5bce-0ab7-9f1f-c9d4ec3b8b81"
}
@BOOK{Williams2001-wy,
title = "Weighing the Odds: A Course in Probability and Statistics",
author = "Williams, David",
abstract = "In this lively look at both subjects, David Williams convinces
Mathematics students of the intrinsic interest of Statistics
and Probability, and Statistics students that the language of
Mathematics can bring real insight and clarity to their
subject. He helps students build the intuition needed, in a
presentation enriched with examples drawn from all manner of
applications. Statistics chapters present both the Frequentist
and Bayesian approaches, emphasizing Confidence Intervals
rather than Hypothesis Test, and include Gibbs-sampling
techniques for the practical implementation of Bayesian
methods. A central chapter gives the theory of Linear
Regression and ANOVA, and explains how MCMC methods allow
greater flexibility in modeling. C or WinBUGS code is provided
for computational examples and simulations.",
publisher = "Cambridge University Press",
month = aug,
year = 2001,
keywords = "PhD",
original_id = "caa71581-bb98-00d8-bd47-7e96f87dcdc8"
}
% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Wong1995-wv,
title = "Probability Inequalities for Likelihood Ratios and Convergence
Rates of Sieve {MLES}",
author = "Wong, Wing Hung and Shen, Xiaotong",
abstract = "Let Y1,..., Yn be independent identically distributed with
density p0 and let F be a space of densities. We show that the
supremum of the likelihood ratios $\prod^n_\{i=1\}
p(Y_i)/p_0(Y_i)$, where the supremum is over p $\in$ F with
|p1/2 - p1/2 0|2 $\geq$ $\epsilon$, is exponentially small
with probability exponentially close to 1. The exponent is
proportional to n$\epsilon$2. The only condition required for
this to hold is that $\epsilon$ exceeds a value determined by
the bracketing Hellinger entropy of F. A similar inequality
also holds if we replace F by Fn and p0 by qn, where qn is an
approximation to p0 in a suitable sense. These results are
applied to establish rates of convergence of sieve MLEs.
Furthermore, weak conditions are given under which the
``optimal'' rate $\epsilon$n defined by H($\epsilon$n, F) =
n$\epsilon$2 n, where H(·, F) is the Hellinger entropy of F,
is nearly achievable by sieve estimators.",
journal = "Ann. Stat.",
publisher = "Institute of Mathematical Statistics",
volume = 23,
number = 2,
pages = "339--362",
year = 1995,
keywords = "PhD",
original_id = "c664fd90-95c5-0030-a902-95fdaa4dcf1c"
}
% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Van_de_Geer1993-qx,
title = "{Hellinger-Consistency} of Certain Nonparametric Maximum
Likelihood Estimators",
author = "van de Geer, Sara",
abstract = "Consider a class P=P$\vartheta$:$\vartheta$$\in$$\Theta$ of
probability measures on a measurable space (X,A), dominated by
a $\sigma$ -finite measure $\mu$. Let
f$\vartheta$=dP$\vartheta$/d$\mu$, $\vartheta$ in$\Theta$, and
let $\vartheta$n be a maximum likelihood estimator based on n
independent observations from P$\vartheta$0 ,
$\vartheta$0$\in$$\Theta$. We use results from empirical
process theory to obtain convergence for the Hellinger
distance h(f$\vartheta$̂n , f$\vartheta$0 ), under certain
entropy conditions on the class of densities
f$\vartheta$:$\vartheta$$\in$$\Theta$ The examples we present
are a model with interval censored observations, smooth
densities, monotone densities and convolution models. In most
examples, the convexity of the class of densities is of
special importance.",
journal = "Ann. Stat.",
publisher = "Institute of Mathematical Statistics",
volume = 21,
number = 1,
pages = "14--44",
year = 1993,
keywords = "PhD",
original_id = "93f3d24d-3f87-048a-bd74-107d930de7e9"
}
@ARTICLE{Silverman1978-oe,
title = "Density Ratios, Empirical Likelihood and Cot Death",
author = "Silverman, B W",
abstract = "A method is developed for the estimation of the logarithm of
the ratio of two probility density functions. The method has
applications in several contexts, notably in data analysis and
inthe construction of empirical versions of statistical
procedures based on likelihood ratios. In this paper, the
method is to a problem arising from the investigation of the
causes of ''cot death''.",
journal = "J. R. Stat. Soc. Ser. C Appl. Stat.",
publisher = "[Wiley, Royal Statistical Society]",
volume = 27,
number = 1,
pages = "26--33",
year = 1978,
keywords = "PhD",
original_id = "324209c0-4eb4-07d3-8a38-97e04299dcab"
}
@ARTICLE{Doosti2016-wy,
title = "Making a non-parametric density estimator more attractive, and
more accurate, by data perturbation",
author = "Doosti, Hassan and Hall, Peter",
abstract = "Summary Motivated by both the shortcomings of high order
density estimators, and the increasingly large data sets in
many areas of modern science, we introduce new high order,
non-parametric density estimators that are guaranteed to be
positive and do not have highly oscillatory tails. Our
approach is based on data perturbation, eg by tilting or data
sharpening. It leads to new estimators that are more accurate
than conventional kernel techniques that ...",
journal = "J. R. Stat. Soc. Series B Stat. Methodol.",
publisher = "Wiley Online Library",
volume = 78,
number = 2,
pages = "445--462",
year = 2016,
keywords = "PhD",
original_id = "fc0806b9-0880-0cbf-9497-2c8e8e2d41e8"
}
% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Liu2004-aw,
title = "Asymptotics for the likelihood ratio test in a two-component
normal mixture model",
author = "Liu, Xin and Shao, Yongzhao",
abstract = "This paper characterizes the asymptotic properties of the
likelihood ratio test (LRT) statistic for testing homogeneity
in a two-component normal mean mixture model. We justify that
the LRT statistic 2$\lambda$n is asymptotically equivalent to
the square of the supremum of the stochastic process studied
in Bickel and Chernoff (Statistics and Probability: A Raghu
Raj Bahadur Festschrift (1993) 83). In particular, we prove
that 2$\lambda$n diverges to +$\infty$ at a rate of log log n
which confirms a conjecture of Hartigan (Proceedings of
Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer
(1985)). More specifically, under the null hypothesis we prove
the following fact:limn$\rightarrow$$\infty$
P\{2$\lambda$n−log log n+log(2$\pi$2)⩽x\}=exp(−e−x/2),
x$\in$R.",
journal = "J. Stat. Plan. Inference",
volume = 123,
number = 1,
pages = "61--81",
month = jun,
year = 2004,
keywords = "Asymptotic distribution; Gaussian mixture model; Homogeneity
test; Likelihood ratio test;PhD",
original_id = "a8fb3b6a-4182-0f66-85f5-aa3298d58ff3"
}
@ARTICLE{Elfving1947-te,
title = "The asymptotical distribution of range in samples from a
normal population",
author = "Elfving, G",
journal = "Biometrika",
volume = 34,
number = "1-2",
pages = "111--119",
year = 1947,
keywords = "POPULATION;PhD",
language = "en",
original_id = "e65d6a10-9f1f-0ff7-b107-e32ffa94e7f4"
}
@ARTICLE{Cox1948-ft,
title = "A Note on the Asymptotic Distribution of Range",
author = "Cox, D R",
journal = "Biometrika",
publisher = "[Oxford University Press, Biometrika Trust]",
volume = 35,
number = "3/4",
pages = "310--315",
year = 1948,
keywords = "PhD",
original_id = "f92b2330-15bc-0f3c-8bc7-f2fc9f71ff99"
}
@INCOLLECTION{David2004-bk,
title = "Order Statistics",
booktitle = "Encyclopedia of Statistical Sciences",
author = "David, H A and Nagaraja, H N",
abstract = "The basic distribution theory of order statistics (ordered
random variables) is developed for both finite random samples
and asymptotically. The use of order statistics in the
estimation of parameters is described, with special emphasis
on suitably chosen linear functions of these variables. Order
statistics provide simple robust estimators of location, such
as the median or trimmed means. They are also useful, as
outlined below, in the treatment of outliers, simultaneous
inference, data compression, probability plotting, ranked-set
sampling, and ranking and selection.",
publisher = "John Wiley \& Sons, Inc.",
year = 2004,
keywords = "distribution of order statistics; linear functions of order
statistics; extreme-value theory; applications of order
statistics;PhD",
original_id = "6cc0f450-e7bb-02d9-8a98-5063fa947479"
}
@ARTICLE{Sinclair1992-tt,
title = "Improved bounds for mixing rates of Markov chains and
multicommodity flow",
author = "Sinclair, Alistair",
journal = "Comb. Probab. Comput.",
volume = 1,
number = 04,
pages = "351--370",
year = 1992,
keywords = "PhD",
original_id = "0264c0a3-4c03-0513-80c4-6a098c52d83d"
}
@ARTICLE{Lindsay1995-gn,
title = "Statistical {ModellingA} review of semiparametric mixture
models",
author = "Lindsay, Bruce G and Lesperance, Mary L",
abstract = "The literature on semiparametric mixture models has flourished
over the last decade, both in applied and theoretical
journals. In this paper, we review examples of important areas
of application, and summarize some of the recent developments
in maximum likelihood theory, including inference for the
mixing distribution and the structural parameters. The theory
and applications developed to date suggest that semiparametric
mixture models will play an ever expanding role in the field.",
journal = "J. Stat. Plan. Inference",
volume = 47,
number = 1,
pages = "29--39",
month = oct,
year = 1995,
keywords = "PhD",
original_id = "4be871ab-4ed4-0bbc-b0e6-6f22103993bd"
}
@ARTICLE{Ng1968-qd,
title = "A Table of Integrals of the Error Functions",
author = "Ng, Edward W and Geller, Murray",
journal = "Journal of research of the National Bureau of
Standards-B.Mathematical Sciences",
volume = "73B",
number = 1,
month = oct,
year = 1968,
keywords = "PhD",
original_id = "6249b432-dc0a-0965-943f-1f2ce07b29d5"
}
@ARTICLE{Van_Havre2015-hd,
title = "Overfitting Bayesian Mixture Models with an Unknown Number of
Components",
author = "van Havre, Zo{\'e} and White, Nicole and Rousseau, Judith and
Mengersen, Kerrie",
abstract = "This paper proposes solutions to three issues pertaining to
the estimation of finite mixture models with an unknown number
of components: the non-identifiability induced by overfitting
the number of components, the mixing limitations of standard
Markov Chain Monte Carlo (MCMC) sampling techniques, and the
related label switching problem. An overfitting approach is
used to estimate the number of components in a finite mixture
model via a Zmix algorithm. Zmix provides a bridge between
multidimensional samplers and test based estimation methods,
whereby priors are chosen to encourage extra groups to have
weights approaching zero. MCMC sampling is made possible by
the implementation of prior parallel tempering, an extension
of parallel tempering. Zmix can accurately estimate the number
of components, posterior parameter estimates and allocation
probabilities given a sufficiently large sample size. The
results will reflect uncertainty in the final model and will
report the range of possible candidate models and their
respective estimated probabilities from a single run. Label
switching is resolved with a computationally light-weight
method, Zswitch, developed for overfitted mixtures by
exploiting the intuitiveness of allocation-based relabelling
algorithms and the precision of label-invariant loss
functions. Four simulation studies are included to illustrate
Zmix and Zswitch, as well as three case studies from the
literature. All methods are available as part of the R package
Zmix, which can currently be applied to univariate Gaussian
mixture models.",
journal = "PLoS One",
volume = 10,
number = 7,
pages = "e0131739",
month = jul,
year = 2015,
keywords = "PhD",
language = "en",
original_id = "7aee627d-4202-0aba-a9f6-b855742b9c1b"
}
@ARTICLE{Grimmett2009-ol,
title = "Random even graphs",
author = "Grimmett, Geoffrey and Janson, Svante",
journal = "the electronic journal of combinatorics",
volume = 16,
number = "R46",
pages = "1",
year = 2009,
keywords = "PhD",
original_id = "8d75c9a0-0610-0deb-9892-499a669fdee7"
}
@ARTICLE{Henna1985-wz,
title = "On estimating of the number of constituents of a finite
mixture of continuous distributions",
author = "Henna, J{\~o}gi",
abstract = "Summary Suppose that H is a mixture of distributions for a
given family FA necessary and sufficient condition is obtained
under which H is, in fact, a finite mixture. An estimator of
the number of distributions constituting the mixture is
proposed assuming that the mixture is ...",
journal = "Ann. Inst. Stat. Math.",
publisher = "Kluwer Academic Publishers",
volume = 37,
number = 1,
pages = "235--240",
year = 1985,
keywords = "PhD",
language = "en",
original_id = "c7a4ec4e-d1d3-00f1-981a-0090e00226aa"
}
@ARTICLE{Roeder1997-wo,
title = "Practical Bayesian Density Estimation Using Mixtures of
Normals",
author = "Roeder, Kathryn and Wasserman, Larry",
abstract = "Abstract Mixtures of normals provide a flexible model for
estimating densities in a Bayesian framework. There are some
difficulties with this model, however. First, standard
reference priors yield improper posteriors. Second, the
posterior for the number of components in the mixture is not
well defined (if the reference prior is used). Third,
posterior simulation does not provide a direct estimate of the
posterior for the number of components. We present some
practical methods for coping with these problems. Finally, we
give some results on the consistency of the method when the
maximum number of components is allowed to grow with the
sample size.",
journal = "J. Am. Stat. Assoc.",
publisher = "amstat.tandfonline.com",
volume = 92,
number = 439,
pages = "894--902",
year = 1997,
keywords = "Mixtures;PhD",
original_id = "34d7f619-80b8-0a43-9725-30c45545a3d9"
}
@ARTICLE{Depraetere2013-kn,
title = "Order selection in finite mixtures of linear regressions",
author = "Depraetere, Nicolas and Vandebroek, Martina",
journal = "Stat. Papers",
publisher = "Springer Berlin Heidelberg",
volume = 55,
number = 3,
pages = "871--911",
month = jun,
year = 2013,
keywords = "PhD",
language = "en",
original_id = "22afda21-6247-0eda-b6cc-17f486a35899"
}
@ARTICLE{Clarke2016-cn,
title = "A comparison of the L\_2 minimum distance estimator and the
{EM-algorithm} when fitting
\{\textbackslashvarvec\{\{k\}\}\}-component univariate normal
mixtures",
author = "Clarke, Brenton R and Davidson, Thomas and Hammarstrand,
Robert",
journal = "Stat. Papers",
publisher = "Springer Berlin Heidelberg",
pages = "1--20",
month = feb,
year = 2016,
keywords = "PhD",
language = "en",
original_id = "e84bc6aa-5ee5-0911-af10-1b9ec9e1ef2b"
}
@ARTICLE{Roeder1994-pe,
title = "A Graphical Technique for Determining the Number of Components
in a Mixture of Normals",
author = "Roeder, Kathryn",
abstract = "Abstract When a population is assumed to be composed of a
finite number of subpopulations, a natural model to choose is
the finite mixture model. It will often be the case, however,
that the number of component distributions is unknown and must
be estimated. This problem can be difficult; for instance, the
density of two mixed normals is not bimodal unless the means
are separated by at least 2 standard deviations. Hence
modality of the data per se can be an insensitive approach to
component estimation. We demonstrate that a mixture of two
normals divided by a normal density having the same mean and
variance as the mixed density is always bimodal. This analytic
result and other related results form the basis for a
diagnostic and a test for the number of components in a
mixture of normals. The density is estimated using a kernel
density estimator. Under the null hypothesis, the proposed
diagnostic can be approximated by a stationary Gaussian
process. Under the alternative hypothesis, components in the
mixture will express themselves as major modes in the
diagnostic plot. A test for mixing is based on the amount of
smoothing necessary to suppress these large deviations from a
Gaussian process.",
journal = "J. Am. Stat. Assoc.",
volume = 89,
number = 426,
pages = "487--495",
year = 1994,
keywords = "PhD",
original_id = "21a9a732-e316-098c-ba38-b38f15d9a2dc"
}
@ARTICLE{Ray2005-nf,
title = "The Topography of Multivariate Normal Mixtures",
author = "Ray, Surajit and Lindsay, Bruce G",
abstract = "Multivariate normal mixtures provide a flexible method of
fitting high-dimensional data. It is shown that their
topography, in the sense of their key features as a density,
can be analyzed rigorously in lower dimensions by use of a
ridgeline manifold that contains all critical points, as well
as the ridges of the density. A plot of the elevations on the
ridgeline shows the key features of the mixed density. In
addition, by use of the ridgeline, we uncover a function that
determines the number of modes of the mixed density when there
are two components being mixed. A followup analysis then gives
a curvature function that can be used to prove a set of
modality theorems.",
journal = "Ann. Stat.",
publisher = "Institute of Mathematical Statistics",
volume = 33,
number = 5,
pages = "2042--2065",
year = 2005,
keywords = "PhD",
original_id = "ee5debff-195e-0875-8605-cfdacf9265e5"
}
@ARTICLE{Bohning1994-be,
title = "The distribution of the likelihood ratio for mixtures of
densities from the one-parameter exponential family",
author = "B{\"o}hning, Dankmar and Dietz, Ekkehart and Schaub, Rainer
and Schlattmann, Peter and Lindsay, Bruce G",
abstract = "Abstract We here consider testing the hypothesis of
homogeneity against the alternative of a two-component mixture
of densities. The paper focuses on the asymptotic null
distribution of 2 log $\lambda$ n, where $\lambda$ n is the
likelihood ratio statistic. The main result, obtained by
simulation, ...",
journal = "Ann. Inst. Stat. Math.",
publisher = "Kluwer Academic Publishers",
volume = 46,
number = 2,
pages = "373--388",
year = 1994,
keywords = "PhD",
language = "en",
original_id = "0a4db1ae-a21f-02cd-bf37-b56ad89cf5de"
}
@BOOK{Dharmadhikari1988-ki,
title = "Unimodality, Convexity, and Applications",
author = "Dharmadhikari, S and Joag-Dev, K",
publisher = "Elsevier Science",
series = "Probability and Mathematical Statistics",
year = 1988,
keywords = "PhD",
original_id = "6ef44e4e-141f-01b8-ae9f-bfcb9c90606d"
}
% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Ghosal2007-ye,
title = "Posterior convergence rates of Dirichlet mixtures at smooth
densities",
author = "Ghosal, Subhashis and van der Vaart, Aad",
abstract = "We study the rates of convergence of the posterior
distribution for Bayesian density estimation with Dirichlet
mixtures of normal distributions as the prior. The true
density is assumed to be twice continuously differentiable.
The bandwidth is given a sequence of priors which is obtained
by scaling a single prior by an appropriate order. In order to
handle this problem, we derive a new general rate theorem by
considering a countable covering of the parameter space whose
prior probabilities satisfy a summability condition together
with certain individual bounds on the Hellinger metric
entropy. We apply this new general theorem on posterior
convergence rates by computing bounds for Hellinger
(bracketing) entropy numbers for the involved class of
densities, the error in the approximation of a smooth density
by normal mixtures and the concentration rate of the prior.
The best obtainable rate of convergence of the posterior turns
out to be equivalent to the well-known frequentist rate for
integrated mean squared error n−2/5 up to a logarithmic
factor.",
journal = "Ann. Stat.",
publisher = "Institute of Mathematical Statistics",
volume = 35,
number = 2,
pages = "697--723",
month = apr,
year = 2007,
keywords = "Bracketing; Dirichlet mixture; entropy; maximum likelihood;
mixture of normals; posterior distribution; rate of
convergence; sieve;PhD",
original_id = "cfac4aff-5bcb-019f-a1bd-e2d4cbd7538a"
}
@ARTICLE{Ghosal2001-ao,
title = "Entropies and Rates of Convergence for Maximum Likelihood and
Bayes Estimation for Mixtures of Normal Densities",
author = "Ghosal, Subhashis and van der Vaart, Aad W",
abstract = "We study the rates of convergence of the maximum likelihood
estimator (MLE) and posterior distribution in density
estimation problems, where the densities are location or
location-scale mixtures of normal distributions with the scale
parameter lying between two positive numbers. The true density
is also assumed to lie in this class with the true mixing
distribution either compactly supported or having sub-Gaussian
tails. We obtain bounds for Hellinger bracketing entropies for
this class, and from these bounds, we deduce the convergence
rates of (sieve) MLEs in Hellinger distance. The rate turns
out to be (log n)$^\kappa/\sqrt\{n\}$, where $\kappa$$\geq$ 1
is a constant that depends on the type of mixtures and the
choice of the sieve. Next, we consider a Dirichlet mixture of
normals as a prior on the unknown density. We estimate the
prior probability of a certain Kullback-Leibler type
neighborhood and then invoke a general theorem that computes
the posterior convergence rate in terms the growth rate of the
Hellinger entropy and the concentration rate of the prior. The
posterior distribution is also seen to converge at the rate
(log n)$^\kappa/\sqrt\{n\}$ in, where $\kappa$ now depends on
the tail behavior of the base measure of the Dirichlet
process.",
journal = "Ann. Stat.",
publisher = "Institute of Mathematical Statistics",
volume = 29,
number = 5,
pages = "1233--1263",
year = 2001,
keywords = "PhD",
original_id = "367a8b70-6dc7-0a5b-9958-c15019dec2ec"
}
@ARTICLE{De_Gier1999-su,
title = "Exact stationary state for an asymmetric exclusion process
with fully parallel dynamics",
author = "De Gier, J and Nienhuis, B",
abstract = "The exact stationary state of an asymmetric exclusion process
with fully parallel dynamics is obtained using the matrix
product ansatz. We give a simple derivation for the
deterministic case by a physical interpretation of the
dimension of the matrices. We prove the stationarity via a
cancellation mechanism, and by making use of an explicit
representation of the matrix algebra we easily find closed
expressions for the correlation functions in the general
probabilistic case. Asymptotic expressions, obtained by making
use of earlier results, allow us to derive the exact phase
diagram.",
journal = "Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip.
Topics",
volume = 59,
number = "5 Pt A",
pages = "4899--4911",
year = 1999,
keywords = "PhD",
original_id = "8e68a144-4494-0e09-afe7-fa030713a4cd"
}
@ARTICLE{Santen2001-di,
title = "The Asymmetric Exclusion Process revisited: Fluctuations and
Dynamics in the Domain Wall Picture",
author = "Santen, Ludger and Appert, Cecile",
abstract = "We investigate the total asymmetric exclusion process by
analyzing the dynamics of the shock. Within this approach we
are able to calculate the fluctuations of the number of
particles and density profiles not only in the stationary
state but also in the transient regime. We find that the
analytical predictions and the simulation results are in
excellent agreement.",
journal = "J. Stat. Phys.",
publisher = "Springer",
volume = 106,
number = "January",
pages = "187--199",
year = 2001,
keywords = "asymmetric exclusion process; boundary induced phase transi;
domain wall theory; tions; transient regime;PhD",
original_id = "00976c66-3c3d-083f-a4fd-cafb876b2f87"
}
@ARTICLE{Grimmett2010-gt,
title = "Random graphs with forbidden vertex degrees",
author = "Grimmett, Geoffrey and Janson, Svante",
journal = "Random Struct. Algorithms",
pages = "137--175",
year = 2010,
keywords = "even graph; random graph; random-cluster model;PhD",
original_id = "ff60853f-035f-0872-92c0-1a72cb926e9e"
}
@ARTICLE{Liu2011-ke,
title = "Worm Monte Carlo study of the honeycomb-lattice loop model",
author = "Liu, Qingquan and Deng, Youjin and Garoni, Timothy M",
journal = "Nucl. Phys. B",
volume = 846,
number = 2,
pages = "283--315",
month = may,
year = 2011,
keywords = "au; cn; corresponding author; deng; e-mail addresses; edu;
garoni; liu; liuqq; loop model; mail; monte carlo; ms; q; t;
unimelb; ustc; worm algorithm; y; yjdeng;PhD",
original_id = "125a19c8-1332-0194-8f9a-7f43cdcb893b"
}
@INCOLLECTION{LeVeque2007-sq,
title = "Chapter 3 - Elliptic Equations",
booktitle = "Finite Difference Methods for Ordinary and Partial
Differential Equations",
author = "LeVeque, Randall J",
publisher = "SIAM",
volume = 59,
pages = "59--88",
chapter = 3,
year = 2007,
keywords = "PhD",
original_id = "3679d39f-86a2-0b7a-9098-a0135d189224"
}
@BOOK{Casella2002-cr,
title = "Statistical inference",
author = "Casella, George and Berger, Roger L",
publisher = "Duxbury Pacific Grove, CA",
volume = 2,
year = 2002,
keywords = "PhD",
original_id = "1ee992b3-f9aa-02ef-bcfa-a412a82d763d"
}
@ARTICLE{Cooper2006-zd,
title = "Sampling Regular Graphs and a {Peer-to-Peer} Network",
author = "Cooper, Colin and Dyer, Martin and Greenhill, Catherine",
journal = "Comb. Probab. Comput.",
volume = 16,
number = 04,
pages = "557",
month = aug,
year = 2006,
keywords = "PhD",
original_id = "0dd259bc-c744-018a-af55-1c42fae20c1f"
}
@ARTICLE{Greenhill2011-cz,
title = "A polynomial bound on the mixing time of a Markov chain for
sampling regular directed graphs",
author = "Greenhill, Catherine",
journal = "Electron. J. Comb.",
volume = 18,
number = 1,
pages = "234",
year = 2011,