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A U-statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens-Fisher setting

high-dimensional two-sample testing problem

Ahmad, Muhammad Rauf (2012). A U-statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens-Fisher setting.
[Preprint] (Submitted)

Full text not available from this repository.

Abstract

A two-sample test statistic is presented for testing the equality of multivariate mean vectors when the dimension of the vectors, $p$, exceeds the sample sizes, $n_i$, $i = 1, 2$, and the underlying distributions are not necessarily normal. Under mild assumptions on the traces of the covariance matrices of the two independent samples, the test statistic is shown to be asymptotically chi-square distributed when both $p \rightarrow \infty$ and $n_i \rightarrow \infty$. However, the validity of the test statistic when $p$ is fixed but large, including $p > n_i$, and when the data follow multivariate normal distribution, is shown as special cases of the main result. This two-sample chi-square approximation eventually helps us establish the validity of Box's approximation for high-dimensional and non-normal data to a two-sample set up, valid even under Behrens-Fisher setting. The limiting chi-square distribution of the statistic is obtained using the asymptotic theory of degenerate $U$-statistics, and using a result from classical asymptotic theory, the asymptotic limit is further extended to an approximate normal distribution. Both independent and paired sample cases are considered.

Authors/Creators:Ahmad, Muhammad Rauf
Title:A U-statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens-Fisher setting
Subtitle:high-dimensional two-sample testing problem
Series/Journal:Annals of the Institute of Statistical Mathematics (0020-3157)
Year of publishing :2012
Number of Pages:31
ISSN:0020-3157
Language:English
Additional Information:Additional affiliation of the author: Department of Statistics, Uppsala University, Sweden. The full text of this publication is not available for reading until the 28:th of February 2013.
Publication Type:Preprint
Version:Submitted version
Full Text Status:None
Agris subject categories.:U Auxiliary disciplines > U10 Mathematical and statistical methods
Subjects:(A) Swedish standard research categories 2011 > 1 Natural sciences > 101 Mathematics > 10106 Probability Theory and Statistics
Keywords:High-dimensional multivariate inference , Box's approximation, Behrens-Fisher setting, Degenerate U-statistics
URN:NBN:urn:nbn:se:slu:epsilon-e-589
Permanent URL:
http://urn.kb.se/resolve?urn=urn:nbn:se:slu:epsilon-e-589
ID Code:9001
Department:(NL, NJ) > Dept. of Energy and Technology
Deposited By: Mr. M. Rauf Ahmad
Deposited On:28 Aug 2012 07:40
Metadata Last Modified:02 Dec 2014 10:51

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