Almost sure convergence for weighted sums of φ-mixing random variables with applications

Research output: Contribution to journalReview article

Abstract

For a sequence {x n , n ≥ 1} of φ-mixing random variables and a triangular array of constants {a n ,k,1≤k≤n,n≥ 1} conditions are given to ensure that (Formula presented.) where {b n } is a prescribed sequence of positive constants. Our statements are established at the extension of a Rosenthal type inequality for φ-mixing random variables and discard any assumption on the mixing coefficient. The proposed results are employed in well-known estimators arising from regression models in order to obtain its strong consistency.

Original languageEnglish
Pages (from-to)3882-3894
JournalCommunications in Statistics - Theory and Methods
Volume49
Issue number16
DOIs
Publication statusPublished - 17 Aug 2020

Keywords

  • mixing
  • strong consistency
  • weighted sum

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