BUG: SeriesGroupBy.nunique raises when grouping with an empty categrorical

doc/source/whatsnew/v2.0.0.rst

@@ -773,6 +773,7 @@ Groupby/resample/rolling
 - Bug in :meth:`.DataFrameGroupBy.describe` would describe the group keys (:issue:`49256`)
 - Bug in :meth:`.SeriesGroupBy.describe` with ``as_index=False`` would have the incorrect shape (:issue:`49256`)
 - Bug in :class:`.DataFrameGroupBy` and :class:`.SeriesGroupBy` with ``dropna=False`` would drop NA values when the grouper was categorical (:issue:`36327`)
+- Bug in :meth:`.SeriesGroupBy.nunique` would incorrectly raise when the grouper was an empty categorical and ``observed=True`` (:issue:`21334`)
 
 Reshaping
 ^^^^^^^^^

pandas/core/groupby/generic.py

@@ -585,7 +585,9 @@ def nunique(self, dropna: bool = True) -> Series:
         # we might have duplications among the bins
         if len(res) != len(ri):
             res, out = np.zeros(len(ri), dtype=out.dtype), res
-            res[ids[idx]] = out
+            if len(ids) > 0:
+                # GH#21334s
+                res[ids[idx]] = out
 
         result = self.obj._constructor(res, index=ri, name=self.obj.name)
         return self._reindex_output(result, fill_value=0)

pandas/tests/groupby/test_nunique.py

@@ -182,3 +182,16 @@ def test_nunique_transform_with_datetime():
     result = df.groupby([0, 0, 1])["date"].transform("nunique")
     expected = Series([2, 2, 1], name="date")
     tm.assert_series_equal(result, expected)
+
+
+def test_empty_categorical(observed):
+    # GH#21334
+    cat = Series([1]).astype("category")
+    ser = cat[:0]
+    gb = ser.groupby(ser, observed=observed)
+    result = gb.nunique()
+    if observed:
+        expected = Series([], index=cat[:0], dtype="int64")
+    else:
+        expected = Series([0], index=cat, dtype="int64")
+    tm.assert_series_equal(result, expected)