Test of Hypotheses Based on the Weighted Likelihood Methodology

Weighted versions of the likelihood ratio, Wald, score and disparity tests are proposed for parametric inference. If the parametric model is correct, the weighted likelihood tests are asymptotically equivalent to the corresponding likelihood based tests, while the disparity test has asymptotically the same distribution as that of ∑p i=1 λiZ 2 i , where Zi are standard normal random variables and λi are eigenvalues of an appropriate matrix. The tests have high level and power breakdown points and they perform well in finite samples. A simulation study and a data example illustrate the performance of the tests in the presence of symmetric and asymmetric contamination.