Statistica Sinica 6(1996), 499-507

ALMOST SURE CONVERGENCE OF WEIGHTED SUMS

Xiru Chen, Li-Xing Zhu and Kai-Tai Fang*

Chinese Academy of Sciences and Hong Kong Baptist University*

Abstract: Suppose that e₁,e₂,... are i.i.d. random variables with Ee₁=0 andE|e₁|^r<∞ for some r with 1≤r<2. In this paper, we obtain sufficient conditions for almost sure convergence of the weighted sum and derive that these conditions are necessary in some sense.

Key words and phrases: Almost sure convergence, linear regression, consistency.