The Asymptotic Distributions of the Largest Entries of Sample Correlation Matrices
نویسندگان
چکیده
Let Xn = (xij) 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. LetRn = (ρij) be the p×p sample correlation matrix ofXn; that is, the entry ρij is the usual Pearson’s correlation coefficient between the ith column of Xn and jth column of Xn. For contemporary data both n and p are large. When the population is a multivariate normal we study the test that H0 : the p variates of the population are uncorrelated. A test statistic is chosen as Ln =maxi6=j |ρij |. The asymptotic distribution of Ln is derived by using the Chen–Stein Poisson approximation method. Similar results for the non-Gaussian case are also derived.
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