Asymptotically refined score and GOF tests for inverse Gaussian models

ABSTRACT

The score test and the GOF test for the inverse Gaussian distribution, in particular the latter, are known to have large size distortion and hence unreliable power when referring to the asymptotic critical values. We show in this paper that with the appropriately bootstrapped critical values, these tests become second-order accurate, with size distortion being essentially eliminated and power more reliable. Two major generalizations of the score test are made: one is to allow the data to be right-censored, and the other is to allow the existence of covariate effects. A data mapping method is introduced for the bootstrap to be able to produce censored data that are conformable with the null model. Monte Carlo results clearly favour the proposed bootstrap tests. Real data illustrations are given.

KEYWORDS:

• Bootstrap critical value
• data mapping
• goodness of fit
• score test
• inverse Gaussian regression
• right-censoring
• Wiener process

AMS SUBJECT CLASSIFICATION:

• 62F03
• 62F05
• 62F40
• 62N01

Acknowledgments

The authors are grateful to an associate editor and two anonymous referees for their helpful comments. Zhenlin Yang gratefully acknowledges the research support from Singapore Management University. He thanks the Dept. of Math. and Stat., University of Guelph, for the support and hospitality during his visit in Oct. 2014

Disclosure statement

No potential conflict of interest was reported by the authors.