Asymptotic distribution of the largest off-diagonal entry of correlation matrices

Author:
Wang Zhou

Journal:
Trans. Amer. Math. Soc. **359** (2007), 5345-5363

MSC (2000):
Primary 60F05, 62G20, 62H10

Published electronically:
May 11, 2007

MathSciNet review:
2327033

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Abstract | References | Similar Articles | 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 Chen-Stein 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:
https://doi.org/10.1090/S0002-9947-07-04192-X

Keywords:
Sample correlation matrices,
Spearman's rank correlation matrices,
Chen-Stein 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 R-155-000-035-112 and R-155-050-055-133/101 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.