Rates of convergence of powered order statistics from general error distribution

Yuhan Zou, Yingyin Lu and Zuoxiang Peng

Statistical Theory and Related Fields, 2023, vol. 7, issue 1, 1-29

Abstract: Let $ \{X_{n}: n\ge 1\} $ {Xn:n≥1} be a sequence of independent random variables with common general error distribution $ \hbox{GED} (v) $ GED(v) with shape parameter v>0, and let $ M_{n,r} $ Mn,r denote the r-th largest order statistics of $ X_{1}, X_{2}, \ldots, X_{n} $ X1,X2,…,Xn. With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics $ |M_{n,r}|^{p} $ |Mn,r|p are established. An alternative method is presented to estimate the probability of the r-th extremes. Numerical analyses are provided to support the main results.

Date: 2023
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DOI: 10.1080/24754269.2022.2146955

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