Abstract: Consider the multiple regression model yn=Σiβix ni+εn, n=1,2,..., where the εn are unobservable random errors; β1,...,βp are unknown parameters and yn is the observed response corresponding to the design vector xn=(xn1,...,xnp)' . Lai & Wei (1982) established results concerning the strong consistency and asymptotic normality of the least squares estimate ofwhere {εn} 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.
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