ASYMPTOTIC NORMALITY FOR EIGENVALUE STATISTICS OF A GENERAL SAMPLE COVARIANCE MATRIX WHEN p/n? 8 AND APPLICATIONS

Qiu, Jiaxin1; Li, Zeng2; Yao, Jianfeng3

2023-06-01

10.1214/23-AOS2300

ANNALS OF STATISTICS   Impact Factor & Quartile

0090-5364

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultrahigh-dimensional setting, that is, when the dimension to sample size ratio p/n & RARR; & INFIN;. Based on this CLT result, we extend the covariance matrix test problem to the new ultra-high-dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the general asymptotic normality of eigenvalue statistics, as well as the two developed tests.

Asymptotic normality linear spectral statistics general sample covariance matrix ultra-dimension matrix white noise separable covariance

SCI

English

Others

NSFC (National Natural Science Founda-tion of China)[12031005] ; NSFC[JCYJ20220818100602005] ; null[12101292]

Mathematics

Statistics & Probability

WOS:001055382500019

INST MATHEMATICAL STATISTICS-IMS

MATHEMATICS

Web of Science

1.Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Peoples R China
2.Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen, Peoples R China
3.Chinese Univ Hong Kong Shenzhen, Sch Data Sci, Shenzhen, Peoples R China

Qiu, Jiaxin,Li, Zeng,Yao, Jianfeng. ASYMPTOTIC NORMALITY FOR EIGENVALUE STATISTICS OF A GENERAL SAMPLE COVARIANCE MATRIX WHEN p/n? 8 AND APPLICATIONS[J]. ANNALS OF STATISTICS,2023,51(3).

Qiu, Jiaxin,Li, Zeng,&Yao, Jianfeng.(2023).ASYMPTOTIC NORMALITY FOR EIGENVALUE STATISTICS OF A GENERAL SAMPLE COVARIANCE MATRIX WHEN p/n? 8 AND APPLICATIONS.ANNALS OF STATISTICS,51(3).

Qiu, Jiaxin,et al."ASYMPTOTIC NORMALITY FOR EIGENVALUE STATISTICS OF A GENERAL SAMPLE COVARIANCE MATRIX WHEN p/n? 8 AND APPLICATIONS".ANNALS OF STATISTICS 51.3(2023).