Abstract
Let X n = (x ij) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R n = (ρ ij) be the p × p sample correlation matrix of X n; that is, the entry ρ ij is the usual Pearson's correlation coefficient between the ith column of X n and jth column of X n. For contemporary data both n and p are large. When the population is a multivariate normal we study the test that H 0 : the p variates of the population are uncorrelated. A test statistic is chosen as L n = max i ≠ j |ρ ij|. The asymptotic distribution of L n is derived by using the Chen-Stein Poisson approximation method. Similar results for the non-Gaussian case are also derived.
Original language | English (US) |
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Pages (from-to) | 865-880 |
Number of pages | 16 |
Journal | Annals of Applied Probability |
Volume | 14 |
Issue number | 2 |
DOIs | |
State | Published - May 2004 |
Keywords
- Chen-Stein method
- Maxima
- Moderate deviations
- Sample correlation matrices