BUG: DataFrame.mode index dtype is not type stable

[TomAugspurger]

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• I have confirmed this bug exists on the latest version of pandas.

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Code Sample, a copy-pastable example

The .index.dtype is not stable for DataFrame.mode. It depends on whether the DataFrame is empty and possible the dtypes

In [60]: pd.DataFrame([], columns=['a', 'b']).mode().index.dtype
Out[60]: dtype('O')

Problem description

The index dtype should always be Int64, to match the non-empty case

Expected Output

In [61]: pd.DataFrame({"A": ['a']}).mode().index.dtype
Out[61]: dtype('int64')

[gregorylivschitz]

@TomAugspurger

This is happening because the empty dataframe returns an empty index and therefore the dtype is dtype('o'):

pd.DataFrame([], columns=['a', 'b']).index.dtype
dtype('O')

pd.DataFrame({"A": ['a']}).index.dtype
dtype('int64')

So there are 2 solutions I can think of.

1. We change mode when it's an empty dataframe to return a dataframe where the mode for that is actually NaN.
   So go from:

pd.DataFrame([], columns=['a', 'b']).mode()
Empty DataFrame
Columns: [a, b]
Index: []

To something like:

pd.DataFrame([], columns=['a', 'b']).mode()
   a    b      
0  NaN  NaN

2. We change what empty dataframe returns when index is called.

Do you like any of those solutions?

[TomAugspurger]

We can construct an empty index with the right dtype (int64)

In [5]: pd.DataFrame(columns=['a', 'b'], index=pd.Index([], dtype='int64')).index.dtype
Out[5]: dtype('int64')