Almost sure convergence of weighted sums

Xiru Chen, Lixing ZHU, Kai Tai Fang

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

Suppose that e1,e2,... are i.i.d. random variables with Ee1 = 0 and E|e1|r < ∞ for some r with 1 ≤ r < 2. In this paper, we obtain sufficient conditions for almost sure convergence of the weighted sum ∑i=1n a(i)ei/A(n) and derive that these conditions are necessary in some sense.

Original languageEnglish
Pages (from-to)499-507
Number of pages9
JournalStatistica Sinica
Volume6
Issue number2
Publication statusPublished - 1996

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Almost sure convergence
  • Consistency
  • Linear regression

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