Asymptotics and bootstrap for inverse Gaussian regression

Gutti Jogesh Babu, Yogendra P. Chaubey

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

This paper studies regression, where the reciprocal of the mean of a dependent variable is considered to be a linear function of the regressor variables, and the observations on the dependent variable are assumed to have an inverse Gaussian distribution. The large sample theory for the pseudo maximum likelihood estimators is available in the literature, only when the number of replications increase at a fixed rate. This is inadequate for many practical applications. This paper establishes consistency and derives the asymptotic distribution for the pseudo maximum likelihood estimators under very general conditions on the design points. This includes the case where the number of replications do not grow large, as well as the one where there are no replications. The bootstrap procedure for inference on the regression parameters is also investigated.

Original languageEnglish (US)
Pages (from-to)75-88
Number of pages14
JournalAnnals of the Institute of Statistical Mathematics
Volume48
Issue number1
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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