On the Variability of the Sample Covariance Matrix Under Complex Elliptical Distributions

Elias Raninen; Esa Ollila; David E. Tyler

doi:10.1109/LSP.2021.3117443

On the Variability of the Sample Covariance Matrix Under Complex Elliptical Distributions

Elias Raninen, Esa Ollila, David E. Tyler

Esa Ollila Group

Rutgers the State University, New Jersey, USA

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

2 Sitaatiot (Scopus)

60 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Artikkeli	9557837
Sivut	2092-2096
Sivumäärä	5
Julkaisu	IEEE Signal Processing Letters
Vuosikerta	28
DOI - pysyväislinkit	https://doi.org/10.1109/LSP.2021.3117443
Tila	Julkaistu - 1 tammik. 2021
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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10.1109/LSP.2021.3117443Lisenssi: CC BY

On_the_Variability_of_the_Sample_Covariance_Matrix_Under_Complex_Elliptical_DistributionsFinal published version, 174 KBLisenssi: CC BY

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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 - Covariance matrices

KW - Random variables

KW - Gaussian distribution

KW - Symmetric matrices

KW - Reactive power

KW - Radar signal processing

KW - Maximum likelihood estimation

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On the Variability of the Sample Covariance Matrix Under Complex Elliptical Distributions

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