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- W2185583313 abstract "For an iid standard normal sample of size n, the article first provides bounds on the expectation and the median of the sample maximum X(n) that are valid for all fixed n ≥ n0 for a small n0, for example n0 = 7. These fixed n bounds on the expectation and the median are derived by first deriving bounds on the standard normal quantile function Φ−1(1−p) itself. The bounds resemble terms in the Edgeworth expansion for the CDF of a sample mean, in an appropriate sense. They are the currently best available explicit nonasymptotic bounds, and are of the correct asymptotic order up to the number of terms present in the given bounds. Next, the article gives exact three term asymptotic expansions for the expectation and median of X(n). This is done by a technique of reducing the extreme value problem to a problem about sample means. This technique is general, and should apply to other distributions. A potential application of a subset of our results is made to the Donoho-Johnstone estimate for the problem of detecting sparse weak signals." @default.
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- W2185583313 date "2012-01-01" @default.
- W2185583313 modified "2023-10-18" @default.
- W2185583313 title "Sharp Nonasymptotic Bounds and Three Term Asymptotic Expansions for the Mean and the Median of a Gaussian Sample Maximum" @default.
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