_reduce needs to be defined on non-NumPy ExtensionArrays

[xhochy]

Creating a Series that is not backed by a NumPy array requires the ExtensionArray object to implement _reduce to correctly delegate the method. The following method reproduces the exception:

import fletcher as fr
import pandas as pd

series = pd.Series(fr.FletcherArray([1, 2]))
series.max()

With the respective exeception:

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-7-f77c98c78d5c> in <module>()
      3 
      4 series = pd.Series(fr.FletcherArray([1, 2]))
----> 5 series.max()

~/Development/arrow-repos-2/pandas/pandas/core/generic.py in stat_func(self, axis, skipna, level, numeric_only, **kwargs)
   9777                                       skipna=skipna)
   9778         return self._reduce(f, name, axis=axis, skipna=skipna,
-> 9779                             numeric_only=numeric_only)
   9780 
   9781     return set_function_name(stat_func, name, cls)

~/Development/arrow-repos-2/pandas/pandas/core/series.py in _reduce(self, op, name, axis, skipna, numeric_only, filter_type, **kwds)
   3251 
-> 3252         return delegate._reduce(op=op, name=name, axis=axis, skipna=skipna,
   3253                                 numeric_only=numeric_only,
   3254                                 filter_type=filter_type, **kwds)

AttributeError: 'FletcherArray' object has no attribute '_reduce'

To fix this bug, I would:

1. Move Categorical._reduce to the ExtensionArray interface.
2. Define a new fixture to specify the supported operations.
3. Add a new class pandas.tests.extension.base.BaseReductionOpsTests to verify the output of these tests.

[jorisvandenbossche]

Yes, we didn't come to this part of the interface yet (the initial use cases did not yet need reducing functions), but is is certainly something we need to add (and will need that as well for the internal extension arrays such as int NA).
See also #21789. So let's use that issues to discuss.

[jorisvandenbossche]

(you can move the example and questions if you want)