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Almost sure convergence of weighted sums. (English) Zbl 0842.62010

Summary: Suppose that \(e_1, e_2, \dots\) are i.i.d. random variables with \(Ee_1=0\) and \(E|e_1|^r< \infty\) for some \(r\) with \(1\leq r< 2\). We obtain sufficient conditions for almost sure convergence of the weighted sum \(\sum^n_{i=1} a(i) e_i/ A(n)\) and derive that these conditions are necessary in some sense.

MSC:

62E20 Asymptotic distribution theory in statistics
62J05 Linear regression; mixed models
60F15 Strong limit theorems
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