<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Modern chromatography largely uses the technique of gas chromatography coupled with mass spectrometry (GC–MS). For a set of data concerning the drought resistance of barley, the problem of the characterization of a covariance structure is investigated with the use of two methods. The first is based on the Frobenius norm and the second on the entropy loss function. For the four considered covariance structures – compound symmetry, three-diagonal and penta-diagonal Toeplitz and autoregression of order one – the Frobenius norm indicates the compound symmetry matrix and autoregression of order one as the most relevant, whilst the entropy loss function gives a slight indication in favor of the compound symmetry structure.</p></abstract>

Modern chromatography largely uses the technique of gas chromatography coupled with mass spectrometry (GC–MS). For a set of data concerning the drought resistance of barley, the problem of the characterization of a covariance structure is investigated with the use of two methods. The first is based on the Frobenius norm and the second on the entropy loss function. For the four considered covariance structures – compound symmetry, three-diagonal and penta-diagonal Toeplitz and autoregression of order one – the Frobenius norm indicates the compound symmetry matrix and autoregression of order one as the most relevant, whilst the entropy loss function gives a slight indication in favor of the compound symmetry structure.

Covariance regularization for metabolomic data on the drought resistance of barley

Department of Mathematical and Statistical Methods

Institute of Plant Genetics, Polish Academy of Sciences

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Modern chromatography largely uses the technique of gas chromatography coupled with mass spectrometry (GC–MS). For a set of data concerning the drought...

Covariance regularization for metabolomic data on the drought resistance of barley

Published Online: Dec 16, 2019

Page range: 165 - 181

DOI: https://doi.org/10.2478/bile-2019-0010

Keywords
covariance structure, compound symmetry matrix, autoregression matrix, Toeplitz matrix, estimation, regularization, entropy loss function, Frobenius norm

© 2019 Adam Mieldzioc et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Covariance regularization for metabolomic data on the drought resistance of barley

Published Online: Dec 16, 2019

Page range: 165 - 181

DOI: https://doi.org/10.2478/bile-2019-0010

Keywordscovariance structure, compound symmetry matrix, autoregression matrix, Toeplitz matrix, estimation, regularization, entropy loss function, Frobenius norm

© 2019 Adam Mieldzioc et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
covariance structure, compound symmetry matrix, autoregression matrix, Toeplitz matrix, estimation, regularization, entropy loss function, Frobenius norm