Unbiased estimators of two second-order moments of the covariance matrix

Volume 8, Issue 1, February 2023     |     PP. 39-50      |     PDF (452 K)    |     Pub. Date: February 9, 2023
DOI: 10.54647/mathematics110384    79 Downloads     2765 Views  

Author(s)

Xuanci Wang, College of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004, China
Wei Yi, Xiamen Second Foreign Language School, Xiamen, Fujian 361100, China
Bin Zhang, College of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004, China

Abstract
The covariance matrix, employed for measuring the linear correlation between variables, plays a vital role in data analysis, such as statistical prediction and hypothesis testing. When the data dimension is high, the traditional sample covariance matrix is not an ideal estimator of the population covariance matrix anymore, resulting in degradation or even inaccuracy of the second-order moment estimators' performance based on the sample covariance matrix. This paper studies the unbiased estimators of the second-order moments under complex Gaussian distribution. The proposed unbiased estimators have better statistical properties and numerical performance than the existing estimation methods.

Keywords
Covariance matrix, second-order moments, complex Gaussian distribution, unbiased estimators

Cite this paper
Xuanci Wang, Wei Yi, Bin Zhang, Unbiased estimators of two second-order moments of the covariance matrix , SCIREA Journal of Mathematics. Volume 8, Issue 1, February 2023 | PP. 39-50. 10.54647/mathematics110384

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