[ENH] implemented anomaly detection _fit_predict override output checks

aeon/testing/estimator_checking/_yield_anomaly_detection_checks.py

@@ -100,3 +100,33 @@ def check_anomaly_detector_output(estimator, datatype):
         ), "y_pred must contain only 0s, 1s, True, or False"
     else:
         raise ValueError(f"Unknown anomaly output type: {ot}")
+
+
+def check_anomaly_detector_fit_predict(estimator, datatype):
+    """Test the anomaly detector fit_predict method."""
+    est1 = _clone_estimator(estimator)
+    est2 = _clone_estimator(estimator)
+    estimator_class = type(estimator)
+
+    # Doesn't proceed if _fit_predict is inherited
+    if "_fit_predict" not in estimator_class.__dict__:
+        return
+
+    fit_predict_output = est1.fit_predict(
+        FULL_TEST_DATA_DICT[datatype]["train"][0],
+        FULL_TEST_DATA_DICT[datatype]["train"][1],
+    )
+    assert isinstance(fit_predict_output, np.ndarray)
+
+    expected_output = est2.fit(
+        FULL_TEST_DATA_DICT[datatype]["train"][0],
+        FULL_TEST_DATA_DICT[datatype]["train"][1],
+    ).predict(FULL_TEST_DATA_DICT[datatype]["train"][0])
+
+    assert isinstance(expected_output, np.ndarray)
+
+    # Assert outputs are same
+    assert len(fit_predict_output) == len(expected_output)
+    assert np.array_equal(
+        fit_predict_output, expected_output
+    ), "outputs of _fit_predict() does not match fit().predict()"