Biometrical Letters

ISSN:1896-3811

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Volume (56) Number 2 pp. 165-181

Adam Mieldzioc 1, Monika Mokrzycka 2

1Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, 60-637, Poznań, Poland
2Institute of Plant Genetics, Polish Academy of Sciences, , 60-479, Poznań, Poland

Covariance regularization for metabolomic data on the drought resistance of barley

Summary

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.

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

DOI: 10.2478/bile-2019-0010

For citation:

MLA Mieldzioc, Adam, and Monika Mokrzycka. "Covariance regularization for metabolomic data on the drought resistance of barley." Biometrical Letters 56.2 (2019): 165-181. DOI: 10.2478/bile-2019-0010
APA Mieldzioc, A., & Mokrzycka, M. (2019). Covariance regularization for metabolomic data on the drought resistance of barley. Biometrical Letters 56(2), 165-181 DOI: 10.2478/bile-2019-0010
ISO 690 MIELDZIOC, Adam, MOKRZYCKA, Monika. Covariance regularization for metabolomic data on the drought resistance of barley. Biometrical Letters, 2019, 56.2: 165-181. DOI: 10.2478/bile-2019-0010