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

• Published in: Computational statistics & data analysis Vol. 55; no. 2; pp. 1109 - 1117
• Main Authors: Lemonte, Artur J., Ferrari, Silvia L.P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2011; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Asymptotic properties; Birnbaum-Saunders distribution Fatigue life distribution Gradient test Lifetime data Likelihood ratio test Local power Score test Wald test; Birnbaum–Saunders distribution; Computer simulation; Crack propagation; Distribution theory; Exact sciences and technology; Fatigue failure; Fatigue life distribution; General topics; Gradient test; Lifetime data; Likelihood ratio test; Local power; Mathematical models; Mathematics; Monte Carlo methods; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Regression; Sciences and techniques of general use; Score test; Statistics; Wald test; Local power; Score test; Wald test; Birnbaum–Saunders distribution; Fatigue life distribution; Likelihood ratio test; Gradient test; Lifetime data; Statistical distribution; Shape parameter; Multivariate analysis; Stochastic method; Birnbaum-Saunders distribution; Hypothesis test; Statistical test; Distribution function; Approximation theory; Life distribution; Likelihood function; Score statistics; Fatigue life; Monte Carlo method; Data analysis; Test statistic; Finite sample; Likelihood ratio; Statistical method; Statistical regression; Lifetime; Numerical analysis; Statistical computation; Asymptotic expansion; Simulation; Regression model; Failure time
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2010.09.008

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 non-null 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 two empirical applications.