CLT for random quadratic forms based on sample means and sample covariance matrices

10/20/2022

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by   Wenzhi Yang, et al.

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In this paper, we use the dimensional reduction technique to study the central limit theory (CLT) random quadratic forms based on sample means and sample covariance matrices. Specifically, we use a matrix denoted by U_p× q, to map q-dimensional sample vectors to a p dimensional subspace, where q≥ p or q≫ p. Under the condition of p/n→ 0 as (p,n)→∞, we obtain the CLT of random quadratic forms for the sample means and sample covariance matrices.