Browse by author
Lookup NU author(s): Dr Jordan Stoyanov
Full text for this publication is not currently held within this repository. Alternative links are provided below where available.
We are interested in the sample maximum X-(n) of an i.i.d standard normal sample of size n. First, we derive two-sided bounds on the mean and the median of X-(n) that are valid for any fixed n >= n(0), where no is 'small', e.g. n(0) = 7. These fixed n bounds are established by using new very sharp bounds on the standard normal quantile function Phi(-1)(1 - p). The bounds found in this paper are currently the best available explicit nonasymptotic bounds, and are of the correct asymptotic order up to the number of terms involved.Then we establish exact three term asymptotic expansions for the mean and the median of X-(n). This is achieved by reducing the extreme value problem to a problem about sample means. This technique is general and should apply to suitable other distributions. One of our main conclusions is that the popular approximation[GRAPHICS]should be discontinued, unless n is fantastically large. Better approximations are suggested in this article. An application of some of our results to the Donoho-Jin sparse signal recovery model is made.The standard Cauchy case is touched on at the very end. (C) 2014 Elsevier B.V. All rights reserved.
Author(s): DasGupta A, Lahiri SN, Stoyanov J
Publication type: Article
Publication status: Published
Journal: Statistical Methodology
Year: 2014
Volume: 20
Pages: 40-62
Print publication date: 14/02/2014
ISSN (print): 1572-3127
ISSN (electronic): 1878-0954
Publisher: Elsevier
URL: http://dx.doi.org/10.1016/j.stamet.2014.01.002
DOI: 10.1016/j.stamet.2014.01.002
Altmetrics provided by Altmetric
