Asymptotic distribution of the largest offdiagonal entry of correlation matrices
Author:
Wang Zhou
Journal:
Trans. Amer. Math. Soc. 359 (2007), 53455363
MSC (2000):
Primary 60F05, 62G20, 62H10
Published electronically:
May 11, 2007
MathSciNet review:
2327033
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: Suppose that we have observations from a dimensional population. We are interested in testing that the variates of the population are independent under the situation where goes to infinity as . A test statistic is chosen to be , where is the sample correlation coefficient between the th coordinate and the th coordinate of the population. Under an independent hypothesis, we prove that the asymptotic distribution of is an extreme distribution of type , by using the ChenStein Poisson approximation method and the moderate deviations for sample correlation coefficients. As a statistically more relevant result, a limit distribution for , where is Spearman's rank correlation coefficient between the th coordinate and the th coordinate of the population, is derived.
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Additional Information
Wang Zhou
Affiliation:
Department of Statistics and Applied Probability, National University of Singapore, Singapore, 117546
Email:
stazw@nus.edu.sg
DOI:
http://dx.doi.org/10.1090/S000299470704192X
PII:
S 00029947(07)04192X
Keywords:
Sample correlation matrices,
Spearman's rank correlation matrices,
ChenStein method,
moderate deviations.
Received by editor(s):
April 25, 2005
Received by editor(s) in revised form:
September 5, 2005
Published electronically:
May 11, 2007
Additional Notes:
The author was supported in part by grants R155000035112 and R155050055133/101 at the National University of Singapore
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
