Statistica Sinica 6(1996), 491-498

A NOTE ON HYPOTHESIS TESTING IN STOCHASTIC

REGRESSION MODELS

Der-Shin Chang and Mei-Rong Chang

National Tsing Hua University

Abstract: Consider the multiple regression model y_n=Σ_iβ_ix _ni+ε_n, n=1,2,..., where the ε_n are unobservable random errors; β₁,...,β_p are unknown parameters and y_n is the observed response corresponding to the design vector x_n=(x_n1,...,x_np)' . Lai & Wei (1982) established results concerning the strong consistency and asymptotic normality of the least squares estimate of where {ε_n} is a martingale difference sequence and some regularity conditions are satisfied. We obtain the same asymptotic normality result under weaker conditions, and also establish the test of linear hypothesis and the strong consistency of the constrained least squares estimate of under .

Key words and phrases: Asymptotic normality, constrained least squares, linear hypothesis, martingales, stochastic regressors, strong consistency.