diff --git a/sklearn/kernel_approximation.py b/sklearn/kernel_approximation.py
index 08957191ba4b8..eb7930f4db319 100644
--- a/sklearn/kernel_approximation.py
+++ b/sklearn/kernel_approximation.py
@@ -83,6 +83,12 @@ class PolynomialCountSketch(BaseEstimator, TransformerMixin):
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
     See Also
     --------
     AdditiveChi2Sampler : Approximate feature map for additive chi2 kernel.
@@ -256,6 +262,12 @@ class RBFSampler(TransformerMixin, BaseEstimator):
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
     See Also
     --------
     AdditiveChi2Sampler : Approximate feature map for additive chi2 kernel.
@@ -386,6 +398,12 @@ class SkewedChi2Sampler(TransformerMixin, BaseEstimator):
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
     See Also
     --------
     AdditiveChi2Sampler : Approximate feature map for additive chi2 kernel.
@@ -520,6 +538,12 @@ class AdditiveChi2Sampler(TransformerMixin, BaseEstimator):
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
     See Also
     --------
     SkewedChi2Sampler : A Fourier-approximation to a non-additive variant of
@@ -764,6 +788,12 @@ class Nystroem(TransformerMixin, BaseEstimator):
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+        .. versionadded:: 1.0
+
     See Also
     --------
     AdditiveChi2Sampler : Approximate feature map for additive chi2 kernel.
diff --git a/sklearn/tests/test_common.py b/sklearn/tests/test_common.py
index 008bdee7e646b..6c2d58266260c 100644
--- a/sklearn/tests/test_common.py
+++ b/sklearn/tests/test_common.py
@@ -327,7 +327,6 @@ def test_check_n_features_in_after_fitting(estimator):
     "compose",
     "ensemble",
     "feature_extraction",
-    "kernel_approximation",
     "model_selection",
     "multiclass",
     "multioutput",
diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index cf88785807d06..5d09b265ee6fc 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -3722,6 +3722,9 @@ def check_dataframe_column_names_consistency(name, estimator_orig):
     set_random_state(estimator)
 
     X_orig = rng.normal(size=(150, 8))
+
+    # Some picky estimators (e.g. SkewedChi2Sampler) only accept skewed positive data.
+    X_orig -= X_orig.min() + 0.5
     X_orig = _enforce_estimator_tags_x(estimator, X_orig)
     X_orig = _pairwise_estimator_convert_X(X_orig, estimator)
     n_samples, n_features = X_orig.shape