Chen, Xiru; Zhu, Li-Xing; Fang, Kai-Tai Almost sure convergence of weighted sums. (English) Zbl 0842.62010 Stat. Sin. 6, No. 2, 499-507 (1996). 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. Cited in 3 ReviewsCited in 8 Documents MSC: 62E20 Asymptotic distribution theory in statistics 62J05 Linear regression; mixed models 60F15 Strong limit theorems Keywords:consistency; sufficient conditions; almost sure convergence; weighted sum PDFBibTeX XMLCite \textit{X. Chen} et al., Stat. Sin. 6, No. 2, 499--507 (1996; Zbl 0842.62010)