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ASYMPTOTICS AND BOOTSTRAP FOR INVERSE

GAUSSIAN REGRESSION

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GUTTI JOGESH BABU^{ 1} AND
YOGENDRA P. CHAUBEY^{ 2}

^{1} *Department of Statistics, 319 Classroom Building,
Pennsylvania State University,*

University Park, PA 16802, U.S.A.

^{2} *Department of Mathematics and Statistics, Concordia
University, Loyola Campus,*

7141 Sherbrooks Street West, Montreal, Quebec, Canada
H4B 1R6
(Received January 13, 1995; revised May 24, 1995)

**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.

*Key words and phrases*:
Chi-square distribution, inverse
Gaussian distribution, *pseudo maximum likelihood*
estimator, strong consistency, weak convergence.

**Source**
( TeX ,
DVI ,
PS )