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

2022/10/20 by Wenzhi Yang, Yiming Liu, Yang, Wenzhi +5
Computer Science · Mathematics · #62E20 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Statistics Theory (math.ST) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2210.11215

openalex publication_date 2022/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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