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<title>Advanced Statistical Theory I-II</title>
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<h2>Advanced Statistical Theory I-II</h2>
<p class="cv-section">Course Description</p>
<p>This course focuses on drawing large sample inferences about "parameters" in statistical models. We develop asymptotic theory for maximum likelihood estimation, M-estimation, and generalized method of moment (GMM) estimation. Formal techniques for constructing estimators in semi-parametric models will be discussed. Particular attention will be paid to models for longitudinal and survival data. Guest lecturers will discuss special topics (e.g., targeted maximum likelihood, hypothesis testing, empirical likelihood). The course will involve rigorous mathematical arguments so that familiarity with concepts in advanced calculus, real analysis, and measure theory will be required. </p>
<p class="cv-section">Intended Audience</p>
<p>The course is designed for Biostatistics Ph.D. students in their 2nd year or beyond. Exceptions made with permission of the instructor.</p>
<p class="cv-section">Prerequisites</p>
<p>Introduction to Probability Theory I-II (550.620-1), Introduction to Statistical Theory I-II (140.673-4), Real Analysis.</p>
<p class="cv-section">Recommended Textbooks</p>
<ul>
<li><u>Theory of Point Estimation</u>, by E.L. Lehmann and G. Casella, Springer</li>
<li><u>A Course in Large Large Sample Theory</u>, by T.S. Ferguson, Chapman-Hall</li>
<li><u>Elements of Large-Sample Theory</u>, by E.L. Lehmann, Springer</li>
<li><u>Approximation Theorems of Mathematical Statistics</u>, by R Serfling, Wiley</li>
<li><u>Asymptotic Statistics</u>, by A.W. van der Vaart, Cambridge</li>
<li><u>Large Sample Estimation and Hypothesis Testing</u>, by W.K. Newey and D. McFadden, Handbook of Econometrics</li>
<li><u>Theoretical Statistics, by D. Cox and D. Hinkley</u>, Chapman and Hall</li>
<li><u>Principles of Mathematical Analysis</u>, by W. Rudin, McGraw Hill</li>
<li><u>Counting Processes and Survival Analysis</u>, by T. Fleming and D. Harrington, Wiley</li>
<li><u>Probability and Measure</u>, by P. Billingsley, Wiley</li>
<li><u>Real Analysis and Probability</u>, by R. Ash, Academic Press</li>
<li><u>Optimization by Vector Space Methods</u>, by D. Luenberger, Wiley</li>
</ul>
<p class="cv-section">Lecture Notes</p>
<ul>
<li>Chapter 1: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture0-1314.pdf" target="_blank">Brief Introduction</a></li>
<li>Chapter 2: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture1-1314.pdf" target="_blank">Analysis and Asymptotics – Review</a></li>
<li>Chapter 3: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture2-1314.pdf" target="_blank">Asymptotic Theory of Estimation</a></li>
<li>Chapter 4.1: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture3-1314.pdf" target="_blank">Asymptotic Properties of the MLE – Part 1</a></li>
<li>Chapter 4.2: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture4-1314.pdf" target="_blank">Asymptotic Properties of the MLE – Part 2</a></li>
<li>Chapter 4.3: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture5-1314.pdf" target="_blank">Asymptotic Properties of the MLE – Part 3</a></li>
<li>Chapter 5: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture6-1314.pdf" target="_blank">Generalized Method of Moments</a></li>
<li>Chapter 6: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture7-1314.pdf" target="_blank">Hilbert Space for Random Vectors</a></li>
<li>Chapter 7: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture8-1314.pdf" target="_blank">Influence Functions</a></li>
<li>Chapter 8: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture9-1314.pdf" target="_blank">Semiparametric Models</a></li>
<li>Chapter 9: <a href="http://www.biostat.jhsph.edu/~dscharf/advinf/lecture11-1314.pdf" target="_blank">Stochastic Processes/Survival Analysis</a></li>
</ul>
<p class="cv-section">Homeworks</p>
<ul>
<li><a href="http://www.biostat.jhsph.edu/~dscharf/advinf/homework1-1415.pdf" target="_blank">HW 1</a></li>
<li><a href="http://www.biostat.jhsph.edu/~dscharf/advinf/homework2-1415.pdf" target="_blank">HW 2</a></li>
<li><a href="http://www.biostat.jhsph.edu/~dscharf/advinf/homework3-1415.pdf" target="_blank">HW 3</a></li>
<li><a href="http://www.biostat.jhsph.edu/~dscharf/advinf/homework4-1415.pdf" target="_blank">HW 4</a></li>
<li><a href="http://www.biostat.jhsph.edu/~dscharf/advinf/homework5-1415.pdf" target="_blank">HW 5</a></li>
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