BUG: min/max of empty datetime dataframe raises

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• I have checked that this issue has not already been reported.

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

• (optional) I have confirmed this bug exists on the master branch of pandas.

Code Sample, a copy-pastable example

import pandas as pd
df = pd.DataFrame(dict(x=pd.to_datetime([])))
df.max()

Traceback (most recent call last):
  File "<ipython-input-17-be9940feb663>", line 1, in <module>
    df.max()
  File "pandas/core/generic.py", line 11215, in stat_func
    f, name, axis=axis, skipna=skipna, numeric_only=numeric_only
  File "pandas/core/frame.py", line 7907, in _reduce
    result = f(values)
  File "pandas/core/frame.py", line 7865, in f
    return op(x, axis=axis, skipna=skipna, **kwds)
  File "pandas/core/nanops.py", line 109, in f
    return _na_for_min_count(values, axis)
  File "pandas/core/nanops.py", line 392, in _na_for_min_count
    result.fill(fill_value)
ValueError: cannot convert float NaN to integer

Problem description

When taking the min/max of an empty datetime dataframe, a ValueError is raised. This is surprising, and inconsistent with the case of an empty datetime series, where min/max return NaT.

Expected Output

x   NaT
dtype: datetime64[ns]

Output of pd.show_versions()

INSTALLED VERSIONS

commit : None
python : 3.7.7.final.0
python-bits : 64
OS : Linux
OS-release : 4.20.11-100.fc28.x86_64
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 1.0.3
numpy : 1.18.1
pytz : 2019.3
dateutil : 2.8.1
pip : 20.0.2
setuptools : 46.1.3.post20200330
Cython : 0.29.15
pytest : 5.4.1
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.5.0
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 2.11.1
IPython : 7.13.0
pandas_datareader: None
bs4 : 4.9.0
bottleneck : 1.3.2
fastparquet : None
gcsfs : None
lxml.etree : 4.5.0
matplotlib : 3.1.3
numexpr : 2.7.1
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 0.15.1
pytables : None
pytest : 5.4.1
pyxlsb : None
s3fs : None
scipy : 1.2.1
sqlalchemy : 1.3.16
tables : 3.6.1
tabulate : None
xarray : None
xlrd : None
xlwt : None
xlsxwriter : None
numba : None

[CloseChoice]

Note the difference here:

In [1]: import pandas as pd                                                                                                                      
# initialize a series from pd.to_datetime
In [2]: srs = pd.Series(pd.to_datetime([]))                                                                                                      

In [3]: srs                                                                                                                                      
Out[3]: Series([], dtype: datetime64[ns])

In [4]: srs.max()                                                                                                                                
Out[4]: NaT

In [5]: df1 = pd.DataFrame(dict(x=pd.to_datetime([])))                                                                                           

In [6]: df1                                                                                                                                      
Out[6]: 
Empty DataFrame
Columns: [x]
Index: []
...
In [8]: df1.max()                                                                                                                                
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-8-ffa8d8284b6e> in <module>
----> 1 df1.max()

~/programming/python/pandas_tests/pandas/pandas/core/generic.py in stat_func(self, axis, skipna, level, numeric_only, **kwargs)
  11172             return self._agg_by_level(name, axis=axis, level=level, skipna=skipna)
  11173         #import pdb; pdb.set_trace()()
> 11174         return self._reduce(
  11175             func, name=name, axis=axis, skipna=skipna, numeric_only=numeric_only
  11176         )

~/programming/python/pandas_tests/pandas/pandas/core/frame.py in _reduce(self, op, name, axis, skipna, numeric_only, filter_type, **kwds)
   8377 
   8378             try:
-> 8379                 result = f(values)
   8380 
   8381             except TypeError:

~/programming/python/pandas_tests/pandas/pandas/core/frame.py in f(x)
   8296 
   8297         def f(x):
-> 8298             return op(x, axis=axis, skipna=skipna, **kwds)
   8299 
   8300         def _get_data(axis_matters):

~/programming/python/pandas_tests/pandas/pandas/core/nanops.py in f(values, axis, skipna, **kwds)
    111                 # correctly handle empty inputs and remove this check.
    112                 # It *may* just be `var`
--> 113                 return _na_for_min_count(values, axis)
    114 
    115             if _USE_BOTTLENECK and skipna and _bn_ok_dtype(values.dtype, bn_name):

~/programming/python/pandas_tests/pandas/pandas/core/nanops.py in _na_for_min_count(values, axis)
    386         result_shape = values.shape[:axis] + values.shape[axis + 1 :]
    387         result = np.empty(result_shape, dtype=values.dtype)
--> 388         result.fill(fill_value)
    389         return result
    390 

ValueError: cannot convert float NaN to integer

# initializing dataframe with an empty list of pandas datetimes
In [9]: df2 = pd.DataFrame([pd.to_datetime([])])                                                                                                 

In [10]: df2                                                                                                                                     
Out[10]: 
Empty DataFrame
Columns: []
Index: [0]

In [11]: df2.max()                                                                                                                               
Out[11]: Series([], dtype: float64)

# when only column x is taken
In [13]: df1.x.max()                                                                                                                             
Out[13]: NaT

This totally seems unexpected, especially [13].