Statistica Sinica 11(2001), 499-514

TEST OF HYPOTHESES BASED ON THE WEIGHTED

LIKELIHOOD METHODOLOGY

Claudio Agostinelli and Marianthi Markatou

University of Padua and Columbia University

Abstract: 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 $\sum_{i=1}^p\lambda_iZ_i^2$, where $Z_i$ are standard normal random variables and $\lambda_i$ 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.

Key words and phrases: Asymptotic distribution, breakdown function, likelihood ratio test, robustness, score test, Wald test, weighted likelihood.