Size and power properties of some tests in the Birnbaum-Saunders regression model

TL;DR

This paper derives asymptotic distributions for various statistical tests in the Birnbaum-Saunders regression model, compares their finite-sample performance via simulations, and demonstrates their application to real data.

Contribution

It provides the first asymptotic expansions of likelihood ratio, Wald, score, and gradient tests in the Birnbaum-Saunders regression model, including their finite-sample comparison.

Findings

All four tests have similar asymptotic distributions under the null hypothesis.

Monte Carlo simulations show differences in finite-sample performance among the tests.

The empirical application illustrates the practical use of these tests in real data analysis.

Abstract

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order $n^{-1/2}$ and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present an empirical application.