BUG: groupby.idxmin/idxmax with all NA values should raise

Author: rhshadrach

pandas/_libs/groupby.pyx

@@ -2048,9 +2048,8 @@ def group_idxmin_idxmax(
         group_min_or_max = np.empty_like(out, dtype=values.dtype)
         seen = np.zeros_like(out, dtype=np.uint8)
 
-    # When using transform, we need a valid value for take in the case
-    # a category is not observed; these values will be dropped
-    out[:] = 0
+    # Sentinel for no valid values.
+    out[:] = -1
 
     with nogil(numeric_object_t is not object):
         for i in range(N):

pandas/core/groupby/groupby.py

@@ -1784,7 +1784,7 @@ def array_func(values: ArrayLike) -> ArrayLike:
         new_mgr = data.grouped_reduce(array_func)
         res = self._wrap_agged_manager(new_mgr)
         if how in ["idxmin", "idxmax"]:
-            res = self._wrap_idxmax_idxmin(res)
+            res = self._wrap_idxmax_idxmin(res, how=how, skipna=kwargs["skipna"])
         out = self._wrap_aggregated_output(res)
         return out
 
@@ -5715,10 +5715,17 @@ def _idxmax_idxmin(
         )
         return result
 
-    def _wrap_idxmax_idxmin(self, res: NDFrameT) -> NDFrameT:
+    def _wrap_idxmax_idxmin(
+        self, res: NDFrameT, how: Literal["idxmax", "idxmin"], skipna: bool
+    ) -> NDFrameT:
         index = self.obj.index
         if res.size == 0:
             result = res.astype(index.dtype)
+        elif skipna and res.lt(0).any(axis=None):
+            raise ValueError(
+                f"{type(self).__name__}.{how} with skipna=True encountered all NA "
+                f"value in a group."
+            )
         else:
             if isinstance(index, MultiIndex):
                 index = index.to_flat_index()