Almost sure central limit theorems of the partial sums and maxima from complete and incomplete samples of stationary sequences

Zuoxiang Peng, Bin Tong, Saralees Nadarajah

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let (X n) denote an independent and identically distributed random sequence. Let S n = σ; k = 1 nX k and M n = maxX 1,.., X n be its partial sum and maximum. Suppose that some of the random variables of X 1, X 2,.. can be observed and denote by M n the maximum of observed random variables from the set X 1,.., X n. In this paper, we consider the joint limiting distribution of (M n, M n, S n) and the almost sure central limit theorems related to the random vector (M n, M n, S n). Furthermore, we extend related results to weakly dependent stationary Gaussian sequences. © 2012 World Scientific Publishing Company.
    Original languageEnglish
    Article number1150026
    JournalStochastics and Dynamics
    Volume12
    Issue number3
    DOIs
    Publication statusPublished - Sept 2012

    Keywords

    • Almost sure central limit theorem
    • joint limiting distribution
    • maximum
    • missing observations
    • partial sum
    • stationary Gaussian sequence

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