Biometrical Letters Vol. 56(2), 2019, pp. 165-181
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COVARIANCE REGULARIZATION FOR METABOLOMIC DATA ON THE DROUGHT RESISTANCE OF BARLEY Adam Mieldzioc1, Monika Mokrzycka2, Aneta Sawikowska1,2 1Department of Mathematical and Statistical Methods, Poznan University of Life Sciences, Wojska Polskiego 28, 60-637 Poznan, Poland e-mail: adam.mieldzioc@mail.up.poznan.pl, aneta.sawikowska@mail.up.poznan.pl 2Institute of Plant Genetics, Polish Academy of Sciences, Strzeszynska 34, 60-479 Poznan, Poland, e-mail: mmok@igr.poznan.pl |
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 structure, compound symmetry matrix, autoregression matrix, Toeplitz matrix, estimation, regularization, entropy loss function, Frobenius norm
