ENH: Infer integer-na in infer_dtype

pandas/_libs/lib.pyx

@@ -1250,7 +1250,10 @@ def infer_dtype(value: object, skipna: object=None) -> str:
         if is_integer_array(values):
             return 'integer'
         elif is_integer_float_array(values):
-            return 'mixed-integer-float'
+            if is_integer_na_array(values):
+                return 'integer-na'
+            else:
+                return 'mixed-integer-float'
         return 'mixed-integer'
 
     elif PyDateTime_Check(val):
@@ -1275,7 +1278,10 @@ def infer_dtype(value: object, skipna: object=None) -> str:
         if is_float_array(values):
             return 'floating'
         elif is_integer_float_array(values):
-            return 'mixed-integer-float'
+            if is_integer_na_array(values):
+                return 'integer-na'
+            else:
+                return 'mixed-integer-float'
 
     elif util.is_bool_object(val):
         if is_bool_array(values, skipna=skipna):
@@ -1511,6 +1517,21 @@ cpdef bint is_integer_array(ndarray values):
     return validator.validate(values)
 
 
+cdef class IntegerNaValidator(Validator):
+    cdef inline bint is_value_typed(self, object value) except -1:
+        return util.is_integer_object(value) or util.is_nan(value)
+
+    cdef inline bint is_array_typed(self) except -1:
+        return issubclass(self.dtype.type, np.integer)
+
+
+cdef bint is_integer_na_array(ndarray values):
+    cdef:
+        IntegerNaValidator validator = IntegerNaValidator(len(values),
+                                                          values.dtype)
+    return validator.validate(values)
+
+
 cdef class IntegerFloatValidator(Validator):
     cdef inline bint is_value_typed(self, object value) except -1:
         return util.is_integer_object(value) or util.is_float_object(value)

pandas/core/arrays/integer.py

@@ -186,6 +186,7 @@ def coerce_to_array(values, dtype, mask=None, copy=False):
             "floating",
             "integer",
             "mixed-integer",
+            "integer-na",
             "mixed-integer-float",
         ]:
             raise TypeError(

pandas/core/indexes/base.py

@@ -472,7 +472,7 @@ def __new__(
                         pass
 
                     return Index(subarr, copy=copy, dtype=object, name=name)
-                elif inferred in ["floating", "mixed-integer-float"]:
+                elif inferred in ["floating", "mixed-integer-float", "integer-na"]:
                     from .numeric import Float64Index
 
                     return Float64Index(subarr, copy=copy, name=name)
@@ -1810,7 +1810,7 @@ def is_integer(self):
         return self.inferred_type in ["integer"]
 
     def is_floating(self):
-        return self.inferred_type in ["floating", "mixed-integer-float"]
+        return self.inferred_type in ["floating", "mixed-integer-float", "integer-na"]
 
     def is_numeric(self):
         return self.inferred_type in ["integer", "floating"]
@@ -3119,6 +3119,7 @@ def _convert_scalar_indexer(self, key, kind=None):
                 if self.inferred_type not in [
                     "floating",
                     "mixed-integer-float",
+                    "integer-na",
                     "string",
                     "unicode",
                     "mixed",
@@ -3196,7 +3197,10 @@ def is_int(v):
                     self.get_loc(stop)
                 is_positional = False
         except KeyError:
-            if self.inferred_type == "mixed-integer-float":
+            if (
+                self.inferred_type == "mixed-integer-float"
+                or self.inferred_type == "integer-na"
+            ):
                 raise
 
         if is_null_slicer:

pandas/core/indexes/datetimes.py

@@ -778,6 +778,7 @@ def join(self, other, how="left", level=None, return_indexers=False, sort=False)
             not in (
                 "floating",
                 "integer",
+                "integer-na",
                 "mixed-integer",
                 "mixed-integer-float",
                 "mixed",

pandas/core/indexes/timedeltas.py

@@ -727,6 +727,7 @@ def _is_convertible_to_index(other):
         "floating",
         "mixed-integer",
         "integer",
+        "integer-na",
         "mixed-integer-float",
         "mixed",
     ):

pandas/tests/dtypes/test_inference.py

@@ -577,6 +577,16 @@ def test_integers(self):
         result = lib.infer_dtype(arr, skipna=True)
         assert result == "integer"
 
+    # GH 27392
+    def test_integer_na(self):
+        arr = np.array([1, 2, np.nan, np.nan, 3], dtype="O")
+        result = lib.infer_dtype(arr, skipna=False)
+        assert result == "integer-na"
+
+        arr = np.array([1, 2, 3, np.int64(4), np.int32(5), np.nan], dtype="O")
+        result = lib.infer_dtype(arr, skipna=False)
+        assert result == "integer-na"
+
     def test_deprecation(self):
         # GH 24050
         arr = np.array([1, 2, 3], dtype=object)