Higher-order expansions of powered extremes of normal samples
Wei Zhou, Chengxiu Ling
TL;DR
This paper develops higher-order mathematical expansions for the distributions and densities of powered extremes in standard normal samples, showing how convergence rates depend on the power index, thus refining previous results.
Contribution
It introduces refined higher-order expansions for powered extremes of normal samples, highlighting the influence of the power index on convergence rates.
Findings
Higher-order expansions for distributions and densities are established.
Convergence rates depend on the power index.
Results refine previous findings by Hall (1980).
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.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Statistical Distribution Estimation and Applications · Probability and Risk Models