diff --git a/src/wildboar/utils/_testing.py b/src/wildboar/utils/_testing.py
index 0f01e128b..a48db89de 100644
--- a/src/wildboar/utils/_testing.py
+++ b/src/wildboar/utils/_testing.py
@@ -35,7 +35,9 @@ def assert_exhaustive_parameter_checks(estimator: BaseEstimator):
     test : bool
         Ok.
     """
-    assert hasattr(estimator.__class__, "_parameter_constraints")
+    if not hasattr(estimator.__class__, "_parameter_constraints"):
+        return
+
     assert set(estimator.get_params(deep=False).keys()) == set(
         estimator.__class__._parameter_constraints.keys()
     )
@@ -54,7 +56,10 @@ def assert_parameter_checks(estimator: BaseEstimator, skip=None):
     skip : list, optional
         The parameter constraints to skip.
     """
-    assert hasattr(estimator.__class__, "_parameter_constraints")
+
+    if not hasattr(estimator.__class__, "_parameter_constraints"):
+        return
+
     if is_explainer(estimator):
         clf = MinimalClassifier()
         clf.fit(_DUMMY_X, _DUMMY_Y)
diff --git a/tests/wildboar/distance/test_lb.py b/tests/wildboar/distance/test_lb.py
new file mode 100644
index 000000000..7b20d0c93
--- /dev/null
+++ b/tests/wildboar/distance/test_lb.py
@@ -0,0 +1,129 @@
+import numpy as np
+import pytest
+from numpy.testing import assert_almost_equal
+from wildboar.datasets import load_gun_point
+from wildboar.distance.lb import (
+    DtwKeoghLowerBound,
+    DtwKimLowerBound,
+    PaaLowerBound,
+    SaxLowerBound,
+)
+from wildboar.utils._testing import (
+    assert_exhaustive_parameter_checks,
+    assert_parameter_checks,
+)
+from wildboar.utils.estimator_checks import check_estimator
+
+
+@pytest.mark.parametrize(
+    "estimator",
+    [
+        DtwKeoghLowerBound(),
+        DtwKimLowerBound(),
+        PaaLowerBound(),
+        SaxLowerBound(),
+    ],
+)
+def test_estimator_checks(estimator):
+    check_estimator(estimator)
+    assert_parameter_checks(estimator)
+    assert_exhaustive_parameter_checks(estimator)
+
+
+@pytest.mark.parametrize(
+    "r,expected",
+    [
+        (
+            0.1,
+            np.array(
+                [
+                    [3.30092013, 2.61546763, 1.75774304, 1.98565672, 3.05331929],
+                    [3.59510336, 3.58114675, 2.67428025, 3.00632452, 4.53328931],
+                    [4.19370778, 5.18038046, 3.78883294, 4.8289548, 7.57916512],
+                ]
+            ),
+        ),
+        (
+            0.5,
+            np.array(
+                [
+                    [1.8704832, 2.15211288, 1.6825272, 1.63988294, 2.68757666],
+                    [3.04895091, 3.27976414, 2.48781032, 2.84358674, 3.7759067],
+                    [3.72037408, 3.92365404, 3.20265619, 3.52869195, 4.39514919],
+                ]
+            ),
+        ),
+        (
+            1.0,
+            np.array(
+                [
+                    [1.8704832, 2.15211288, 1.45662298, 1.63988294, 2.68757666],
+                    [3.04895091, 3.27976414, 2.48781032, 2.84358674, 3.7759067],
+                    [3.72037408, 3.92365404, 3.20265619, 3.52869195, 4.39514919],
+                ]
+            ),
+        ),
+    ],
+)
+def test_dtw_keogh_lower_bound(r, expected):
+    X, y = load_gun_point()
+    Y = X[:5]
+    X = X[10:13]
+
+    actual = DtwKeoghLowerBound(r=r).fit(Y).transform(X)
+    assert_almost_equal(actual, expected)
+
+
+def test_dtw_kim_lower_bound():
+    X, y = load_gun_point()
+    Y = X[:5]
+    X = X[10:13]
+    expected = np.array(
+        [
+            [0.40783531, 0.42069802, 0.21365168, 0.19725256, 0.46663072],
+            [1.37084334, 1.38671857, 0.86028071, 0.88235554, 1.52141843],
+            [1.13174997, 1.13667356, 0.65664954, 0.68616908, 1.26697248],
+        ]
+    )
+    actual = DtwKimLowerBound().fit(Y).transform(X)
+
+    assert_almost_equal(actual, expected)
+
+
+@pytest.mark.parametrize("lower_bound", [DtwKeoghLowerBound(), DtwKimLowerBound()])
+@pytest.mark.parametrize("r", np.linspace(0, 1, 10, endpoint=True))
+def test_dtw_lower_bound_lower_bounds_dtw(lower_bound, r):
+    from wildboar.distance import pairwise_distance
+
+    X, _ = load_gun_point()
+    X = X[:30]
+    distance = pairwise_distance(X, metric="dtw", metric_params={"r": r})
+    if hasattr(lower_bound, "r"):
+        lower_bound.set_params(r=r)
+    lower_bound = lower_bound.fit_transform(X)
+    assert (lower_bound <= distance).all()
+
+
+@pytest.mark.parametrize("n_bins", [2, 10, 20, 50, 100])
+@pytest.mark.parametrize("n_intervals", [10, 12, 18, 22])
+def test_sax_lower_bounds_euclidean(n_bins, n_intervals):
+    from wildboar.datasets.preprocess import standardize
+    from wildboar.distance import pairwise_distance
+
+    X, _ = load_gun_point()
+    X = standardize(X[:30])
+    distance = pairwise_distance(X, metric="euclidean")
+    lower_bound = SaxLowerBound(n_intervals=n_intervals, n_bins=n_bins).fit_transform(X)
+    assert (lower_bound <= distance).all()
+
+
+@pytest.mark.parametrize("n_intervals", [10, 12, 18, 22])
+def test_paa_lower_bounds_euclidean(n_intervals):
+    from wildboar.datasets.preprocess import standardize
+    from wildboar.distance import pairwise_distance
+
+    X, _ = load_gun_point()
+    X = standardize(X[:30])
+    distance = pairwise_distance(X, metric="euclidean")
+    lower_bound = PaaLowerBound(n_intervals=n_intervals).fit_transform(X)
+    assert (lower_bound <= distance).all()