On the variability of the sample covariance matrix under complex elliptical distributions

Elias Raninen; Esa Ollila; David Tyler

doi:10.1109/LSP.2021.3117443

On the variability of the sample covariance matrix under complex elliptical distributions

Elias Raninen, Esa Ollila, David Tyler

School of Arts and Sciences, Statistics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented.

Original language	English (US)
Pages (from-to)	2092-2096
Number of pages	5
Journal	IEEE Signal Processing Letters
Volume	28
DOIs	https://doi.org/10.1109/LSP.2021.3117443
State	Published - 2021

All Science Journal Classification (ASJC) codes

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

Keywords

Complex Gaussian distribution
Complex elliptically symmetric distribution
Mean squared error
Sample covariance matrix
Sample variation

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10.1109/LSP.2021.3117443

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abstract = "We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented.",

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AU - Ollila, Esa

AU - Tyler, David

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AB - We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented.

KW - Complex Gaussian distribution

KW - Complex elliptically symmetric distribution

KW - Mean squared error

KW - Sample covariance matrix

KW - Sample variation

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EP - 2096

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

ER -

On the variability of the sample covariance matrix under complex elliptical distributions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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