Higher-order expansions of powered extremes of normal samples

Wei Zhou; Chengxiu Ling

doi:10.1016/j.spl.2016.01.003

Higher-order expansions of powered extremes of normal samples

Wei Zhou
, Chengxiu Ling^*

^*Corresponding author for this work

Southwest University

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	12-17
Number of pages	6
Journal	Statistics and Probability Letters
Volume	111
DOIs	https://doi.org/10.1016/j.spl.2016.01.003
Publication status	Published - 1 Apr 2016
Externally published	Yes

Keywords

Convergence rate
Higher-order expansion
Powered extremes
Primary
Secondary

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10.1016/j.spl.2016.01.003

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title = "Higher-order expansions of powered extremes of normal samples",

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, Primary, Secondary",

author = "Wei Zhou and Chengxiu Ling",

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year = "2016",

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doi = "10.1016/j.spl.2016.01.003",

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AU - Zhou, Wei

AU - Ling, Chengxiu

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N2 - 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.

AB - 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.

KW - Convergence rate

KW - Higher-order expansion

KW - Powered extremes

KW - Primary

KW - Secondary

UR - https://www.scopus.com/pages/publications/85000444163

U2 - 10.1016/j.spl.2016.01.003

DO - 10.1016/j.spl.2016.01.003

M3 - Article

AN - SCOPUS:85000444163

SN - 0167-7152

VL - 111

SP - 12

EP - 17

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Higher-order expansions of powered extremes of normal samples

Abstract

Keywords

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