On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix

  • Authors:

  • Deli Li;Yongcheng Qi;Andrew Rosalsky

  • Affiliations:

  • Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1;Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN 55812, USA;Department of Statistics, University of Florida, Gainesville, FL 32611, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2012

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Abstract

Let {X,X"k","i;i=1,k=1} be a double array of nondegenerate i.i.d. random variables and let {p"n;n=1} be a sequence of positive integers such that n/p"n is bounded away from 0 and ~. This paper is devoted to the solution to an open problem posed in Li et al. (2010) [9] on the asymptotic distribution of the largest entry L"n=max"1"@?"i"~n^2@!"("n"l"o"g"n")"^"1"^"/"^"4^~(F^n^-^1(x)-F^n^-^1(nlognx))dF(x)=0,(2)(nlogn)^1^/^2L"n-P2,(3)limn-~P(nLn2-a"n@?t)=exp{-18@pe^-^t^/^2},-~=0 and a"n=4logp"n-loglogp"n, n=2. To establish this result, we present six interesting new lemmas which may be of independent interest.