STOCHASTIC REGRESSION MODEL WITH HETEROSCEDASTIC DISTURBANCE

DER-SHIN CHANG AND GUAN-CHYUN LIN

Institute of Statistics, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.

(Received February 28, 1994; revised September 12, 1994)

Abstract. This paper discusses some properties of stochastic regression model with continuous form of heteroscedastic disturbance. The strong consistency and asymptotic normality of a generalized weighted least squares estimate will be investigated under certain conditions on the stochastic regressors and errors. More, the linear hypothesis testing problem also be discussed and an example to be demonstrated to reestablish the results of Cheng and Chang (1990, Tech. Report, National Tsing Hua University).

Key words and phrases: Stochastic regressors, generalized weighted least squares, strong consistency, asymptotic normality, linear hypothesis, martingales, heteroscedastic disturbance.