Size and power properties of some tests in the Birnbaum–Saunders regression model
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 distributio...
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| Published in | Computational statistics & data analysis Vol. 55; no. 2; pp. 1109 - 1117 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.02.2011
Elsevier |
| Series | Computational Statistics & Data Analysis |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-9473 1872-7352 |
| DOI | 10.1016/j.csda.2010.09.008 |
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| 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 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. |
|---|---|
| AbstractList | 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. 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 super(-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. 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. |
| Author | Ferrari, Silvia L.P. Lemonte, Artur J. |
| Author_xml | – sequence: 1 givenname: Artur J. surname: Lemonte fullname: Lemonte, Artur J. – sequence: 2 givenname: Silvia L.P. surname: Ferrari fullname: Ferrari, Silvia L.P. email: silviaferrari.usp@gmail.com |
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| Keywords | 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 |
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| Snippet | The Birnbaum–Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data.... The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data.... |
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| SubjectTerms | 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 |
| Title | Size and power properties of some tests in the Birnbaum–Saunders regression model |
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