Asymptotics and bootstrap for inverse Gaussian regression

G. Jogesh Babu, Yogendra P. Chaubey

Research output: Contribution to journalArticle

3 Citations (Scopus)

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

Fingerprint

Inverse Gaussian
Pseudo-maximum Likelihood
Bootstrap
Replication
Regression
Maximum Likelihood Estimator
Large Sample Theory
Inverse Gaussian Distribution
Dependent
Linear Function
Asymptotic distribution

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

@article{2898c4ee01534126a6c9e7c35adc6f56,
title = "Asymptotics and bootstrap for inverse Gaussian regression",
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.",
author = "Babu, {G. Jogesh} and Chaubey, {Yogendra P.}",
year = "1996",
month = "1",
day = "1",
doi = "10.1007/BF00049290",
language = "English (US)",
volume = "48",
pages = "75--88",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer Netherlands",
number = "1",

}

Asymptotics and bootstrap for inverse Gaussian regression. / Babu, G. Jogesh; Chaubey, Yogendra P.

In: Annals of the Institute of Statistical Mathematics, Vol. 48, No. 1, 01.01.1996, p. 75-88.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Asymptotics and bootstrap for inverse Gaussian regression

AU - Babu, G. Jogesh

AU - Chaubey, Yogendra P.

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030352290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030352290&partnerID=8YFLogxK

U2 - 10.1007/BF00049290

DO - 10.1007/BF00049290

M3 - Article

AN - SCOPUS:0030352290

VL - 48

SP - 75

EP - 88

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 1

ER -