科研之友
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摘要
Let X((n)) = (X(ij)) be a p x n data matrix, where the n columns form a random sample of size n from a certain p-dimensional distribution. Let R((n)) = (rho(ij)) be the p x p sample correlation coefficient matrix of X((n)), and S((n)) = (1/n)X((n)) (X((n)))* - (X) over bar(X) over bar* be the sample covariance matrix of X((n)), where (X) over bar is the mean vector of the n observations. Assuming that X(ij) are independent and identically distributed with finite fourth moment, we show that the smallest eigenvalue of R((n)) converges almost surely to the limit (1 - root c)(2) as n -> infinity and p/n -> c is an element of (0, infinity). We accomplish this by showing that the smallest eigenvalue of S((n)) converges almost surely to (1 - root c)(2).
- 出版日期2010-3
