THE QUASI-LIKELIHOOD ESTIMATION IN REGRESSION

JONG-WUU WU

Department of Statistics, Tamkang University, Tamsui, Taipei, Taiwan 25137, R.O.C.

(Received March 10, 1994; revised August 17, 1995)

Abstract. I propose a simply method to estimate the regression parameters in quasi-likelihood model. My main approach utilizes the dimension reduction technique to first reduce the dimension of the regressor X to one dimension before solving the quasi-likelihood equations. In addition, the real advantage of using dimension reduction technique is that it provides a good initial estimate for one-step estimator of the regression parameters. Under certain design conditions, the estimators are asymptotically multivariate normal and consistent. Moreover, a Monte Carlo simulation is used to study the practical performance of the procedures, and I also assess the cost of CPU time for computing the estimates.

Key words and phrases: Regression parameter, quasi-likelihood model, link function, Monte Carlo simulation.