[BUG] add consistency to_numeric on empty list

doc/source/whatsnew/v1.1.0.rst

@@ -232,6 +232,7 @@ Numeric
 ^^^^^^^
 - Bug in :meth:`DataFrame.floordiv` with ``axis=0`` not treating division-by-zero like :meth:`Series.floordiv` (:issue:`31271`)
 - Bug in :meth:`to_numeric` with string argument ``"uint64"`` and ``errors="coerce"`` silently fails (:issue:`32394`)
+- Bug in :meth:`to_numeric` with ``downcast="unsigned"`` fails for empty data (:issue:`32493`)
 -
 
 Conversion

pandas/core/tools/numeric.py

@@ -162,7 +162,7 @@ def to_numeric(arg, errors="raise", downcast=None):
 
         if downcast in ("integer", "signed"):
             typecodes = np.typecodes["Integer"]
-        elif downcast == "unsigned" and np.min(values) >= 0:
+        elif downcast == "unsigned" and (len(values) == 0 or np.min(values) >= 0):
             typecodes = np.typecodes["UnsignedInteger"]
         elif downcast == "float":
             typecodes = np.typecodes["Float"]

pandas/tests/tools/test_to_numeric.py

@@ -627,3 +627,15 @@ def test_non_coerce_uint64_conflict(errors, exp):
     else:
         result = to_numeric(ser, errors=errors)
         tm.assert_series_equal(result, ser)
+
+
+@pytest.mark.parametrize("dc1", ["integer", "float", "unsigned"])
+@pytest.mark.parametrize("dc2", ["integer", "float", "unsigned"])
+def test_downcast_empty(dc1, dc2):
+    # GH32493
+
+    tm.assert_numpy_array_equal(
+        pd.to_numeric([], downcast=dc1),
+        pd.to_numeric([], downcast=dc2),
+        check_dtype=False,
+    )