Ridge estimation of covariance matrix from data in two classes

Yi Zhou; Bin Zhang

Applications of Mathematics (2024)

  • Volume: 69, Issue: 2, page 169-184
  • ISSN: 0862-7940

Abstract

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This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data.

How to cite

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Zhou, Yi, and Zhang, Bin. "Ridge estimation of covariance matrix from data in two classes." Applications of Mathematics 69.2 (2024): 169-184. <http://eudml.org/doc/299252>.

@article{Zhou2024,
abstract = {This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data.},
author = {Zhou, Yi, Zhang, Bin},
journal = {Applications of Mathematics},
keywords = {covariance matrix; ridge estimation; two-class data; contamination},
language = {eng},
number = {2},
pages = {169-184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ridge estimation of covariance matrix from data in two classes},
url = {http://eudml.org/doc/299252},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Zhou, Yi
AU - Zhang, Bin
TI - Ridge estimation of covariance matrix from data in two classes
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 169
EP - 184
AB - This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data.
LA - eng
KW - covariance matrix; ridge estimation; two-class data; contamination
UR - http://eudml.org/doc/299252
ER -

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