Some limit theorems for the eigenvalues of a sample covariance matrix

Dag Jonsson

Journal of Multivariate Analysis, 1982, vol. 12, issue 1, 1-38

Abstract: Limit theorems are given for the eigenvalues of a sample covariance matrix when the dimension of the matrix as well as the sample size tend to infinity. The limit of the cumulative distribution function of the eigenvalues is determined by use of a method of moments. The proof is mainly combinatorial. By a variant of the method of moments it is shown that the sum of the eigenvalues, raised to k-th power, k = 1, 2,..., m is asymptotically normal. A limit theorem for the log sum of the eigenvalues is completed with estimates of expected value and variance and with bounds of Berry-Esseen type.

Keywords: Eigenvalues; of; a; sample; covariance; matrix; cumulative; distribution; function; method; of; moments; limit; theorems; sums; of; eigenvalues; generalized; variance (search for similar items in EconPapers)
Date: 1982
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Citations: View citations in EconPapers (23)

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