diff --git a/test/test_adaptative_permutation_threshold_SVR.py b/test/test_adaptative_permutation_threshold_SVR.py
index b175b51..144e1f1 100644
--- a/test/test_adaptative_permutation_threshold_SVR.py
+++ b/test/test_adaptative_permutation_threshold_SVR.py
@@ -4,9 +4,11 @@
 
 import numpy as np
 from numpy.testing import assert_almost_equal
+from sklearn.svm import SVR
 
 from hidimstat.adaptative_permutation_threshold_SVR import ada_svr, ada_svr_pvalue
 from hidimstat.scenario import multivariate_1D_simulation
+from hidimstat.permutation_test import permutation_test
 
 
 def test_ada_svr():
@@ -42,3 +44,54 @@ def test_ada_svr():
 
     assert_almost_equal(pval[:support_size], expected[:support_size], decimal=1)
     assert_almost_equal(pval_corr[support_size:], expected[support_size:], decimal=1)
+
+
+def test_ada_svr_rcond():
+    """
+    Testing the effect of rcond
+    """
+    # create dataset
+    X, y, beta, _ = multivariate_1D_simulation(
+        n_samples=20,
+        n_features=50,
+        support_size=3,
+        sigma=0.1,
+        shuffle=False,
+        seed=42,
+    )
+    X[:10] *= 1e-5
+    beta_hat, scale = ada_svr(X, y)
+    beta_hat_2, scale_2 = ada_svr(X, y, rcond=1e-15)
+    assert np.max(np.abs(beta_hat - beta_hat_2)) > 1
+    assert np.max(np.abs(scale - scale_2)) > 1
+
+
+def test_ada_svr_vs_permutation():
+    """
+    Validate the adaptive permutation threshold procedure against a permutation
+    test. The adaptive permutation threshold procedure should good approciation
+    of the proba of the permutation test.
+    """
+    # create dataset
+    X, y, beta, _ = multivariate_1D_simulation(
+        n_samples=10,
+        n_features=100,
+        support_size=1,
+        sigma=0.1,
+        shuffle=False,
+        seed=42,
+    )
+    beta_hat, scale = ada_svr(X, y)
+    # fit a SVR to get the coefficients
+    estimator = SVR(kernel="linear", epsilon=0.0, gamma="scale", C=1.0)
+    estimator.fit(X, y)
+    beta_hat_svr = estimator.coef_
+
+    # compare that the coefficiants are the same that the one of SVR
+    assert np.max(np.abs(beta_hat - beta_hat_svr.T[:, 0])) < 2e-4
+
+    proba = permutation_test(
+        X, y, estimator=estimator, n_permutations=10000, n_jobs=8, seed=42, proba=True
+    )
+    assert np.max(np.abs(np.mean(proba, axis=0))) < 1e-3
+    assert np.max(np.abs(scale - np.std(proba, axis=0)) / scale) < 1e-1