Higher-order expansions of powered extremes of normal samples

Wei Zhou and Chengxiu Ling

Statistics & Probability Letters, 2016, vol. 111, issue C, 12-17

Abstract: In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall (1980). Furthermore, it is shown that the rate of convergence of distributions/densities of normalized extremes depends in principle on the power index.

Keywords: Convergence rate; Higher-order expansion; Powered extremes (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2016.01.003

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