Gradient statistic and asymptotic inference in the Birnbaum-Saunders regression model

Author(s)

Artur Jose Lemonte

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2010-02-05

Examining board members

Silvia Lopes de Paula Ferrari; Gauss Moutinho Cordeiro; Francisco Cribari Neto; Gilberto Alvarenga Paula; Klaus Leite Pinto Vasconcellos

• Advisor: Silvia Lopes de Paula Ferrari

Abstract

The Birnbaum-Saunders regression model is commonly used in reliability studies.We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio and score tests tend to be liberal when the sample size is small. We derive Bartlett and Bartlett-type correction factors which reduce the size distortion of the tests. Additionally, we also consider modified signed log-likelihood ratio statistics in this class of models. Finally, the asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n^{-1/2}, n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. (AU)