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Further research on limit theorems for self-normalized sums

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  • Yong Zhang

Abstract

In this paper, we show that self-normalized versions of central limit theorem and almost sure central limit theorem hold with more general weight sequence both for i.i.d. random sequence and ϕ−mixing sequence. Our conclusions generalize and improve the known results from the logarithmic averages which used traditionally in almost sure central limit theorem to some general averages.

Suggested Citation

  • Yong Zhang, 2020. "Further research on limit theorems for self-normalized sums," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(2), pages 385-402, January.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:2:p:385-402
    DOI: 10.1080/03610926.2018.1543767
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    Cited by:

    1. Kaiyu Liang & Yong Zhang, 2024. "Almost Sure Central Limit Theorem for Error Variance Estimator in Pth-Order Nonlinear Autoregressive Processes," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    2. Li, Jingyu & Zhang, Yong, 2021. "An almost sure central limit theorem for the stochastic heat equation," Statistics & Probability Letters, Elsevier, vol. 177(C).

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