Non Null Asymptotic Distributions of Some Criteria in Censored Exponential Regression

Abstract

In this article, we consider the class of censored exponential regression models which is very useful for modeling lifetime data. Under a sequence of Pitman alternatives, the asymptotic expansions up to order n^{− 1/2} of the non null distribution functions of the likelihood ratio, Wald, Rao score, and gradient statistics are derive in this class of models. The non null asymptotic distribution functions of these statistics are obtained for testing a composite null hypothesis in the presence of nuisance parameters. The power of all four tests, which are equivalent to first order, are compared based on these non null asymptotic expansions. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, we consider Monte Carlo simulations. We also present an empirical application for illustrative purposes.

Keywords:

• Asymptotic expansions
• Censored observations
• Exponential models
• Gradient test
• Likelihood ratio test
• Local power
• Score test
• Wald test

Mathematics Subject Clssification:

• 62F03
• 62F05