BUG: dtype of DataFrame.idxmax/idxmin incorrect for empty frames

doc/source/whatsnew/v2.1.0.rst

@@ -432,6 +432,7 @@ Reshaping
 ^^^^^^^^^
 - Bug in :func:`crosstab` when ``dropna=False`` would not keep ``np.nan`` in the result (:issue:`10772`)
 - Bug in :meth:`DataFrame.agg` and :meth:`Series.agg` on non-unique columns would return incorrect type when dist-like argument passed in (:issue:`51099`)
+- Bug in :meth:`DataFrame.idxmin` and :meth:`DataFrame.idxmax`, where the axis dtype would be lost for empty frames (:issue:`53265`)
 - Bug in :meth:`DataFrame.merge` not merging correctly when having ``MultiIndex`` with single level (:issue:`52331`)
 - Bug in :meth:`DataFrame.stack` losing extension dtypes when columns is a :class:`MultiIndex` and frame contains mixed dtypes (:issue:`45740`)
 - Bug in :meth:`DataFrame.transpose` inferring dtype for object column (:issue:`51546`)

pandas/core/frame.py

@@ -11161,6 +11161,11 @@ def idxmin(
         self, axis: Axis = 0, skipna: bool = True, numeric_only: bool = False
     ) -> Series:
         axis = self._get_axis_number(axis)
+
+        if self.empty and len(self.axes[axis]):
+            axis_dtype = self.axes[axis].dtype
+            return self._constructor_sliced(dtype=axis_dtype)
+
         if numeric_only:
             data = self._get_numeric_data()
         else:
@@ -11186,6 +11191,11 @@ def idxmax(
         self, axis: Axis = 0, skipna: bool = True, numeric_only: bool = False
     ) -> Series:
         axis = self._get_axis_number(axis)
+
+        if self.empty and len(self.axes[axis]):
+            axis_dtype = self.axes[axis].dtype
+            return self._constructor_sliced(dtype=axis_dtype)
+
         if numeric_only:
             data = self._get_numeric_data()
         else:

pandas/tests/frame/test_reductions.py

@@ -964,6 +964,18 @@ def test_idxmin(self, float_frame, int_frame, skipna, axis):
             expected = df.apply(Series.idxmin, axis=axis, skipna=skipna)
             tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize("axis", [0, 1])
+    def test_idxmin_empty(self, index, skipna, axis):
+        # GH53265
+        if axis == 0:
+            frame = DataFrame(index=index)
+        else:
+            frame = DataFrame(columns=index)
+
+        result = frame.idxmin(axis=axis, skipna=skipna)
+        expected = Series(dtype=index.dtype)
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize("numeric_only", [True, False])
     def test_idxmin_numeric_only(self, numeric_only):
         df = DataFrame({"a": [2, 3, 1], "b": [2, 1, 1], "c": list("xyx")})
@@ -992,6 +1004,18 @@ def test_idxmax(self, float_frame, int_frame, skipna, axis):
             expected = df.apply(Series.idxmax, axis=axis, skipna=skipna)
             tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize("axis", [0, 1])
+    def test_idxmax_empty(self, index, skipna, axis):
+        # GH53265
+        if axis == 0:
+            frame = DataFrame(index=index)
+        else:
+            frame = DataFrame(columns=index)
+
+        result = frame.idxmax(axis=axis, skipna=skipna)
+        expected = Series(dtype=index.dtype)
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize("numeric_only", [True, False])
     def test_idxmax_numeric_only(self, numeric_only):
         df = DataFrame({"a": [2, 3, 1], "b": [2, 1, 1], "c": list("xyx")})