Convergence of series of moments on general exponential inequality

Research output: Contribution to journalArticlepeer-review

Abstract

For an array (Formula presented.) of random variables and a sequence (Formula presented.) of positive numbers, sufficient conditions are given under which, for all (Formula presented.), (Formula presented.) where (Formula presented.) denotes the positive part of x and (Formula presented.), (Formula presented.). Our statements are announced in a general setting allowing to conclude the previous convergence for well-known dependent structures. As an application, we study complete consistency and consistency in the rth mean of cumulative sum type estimators of the change in the mean of dependent observations.

Original languageEnglish
JournalStatistics
DOIs
Publication statusAccepted/In press - 2022

Keywords

  • convergence of series of moments
  • CUSUM-type estimators
  • dependent random variables
  • Maximum of partial sums

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