A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures

Filipiak, Katarzyna; Klein, Daniel; Roy, Anuradha

doi:10.1002/bimj.201600044

Cited by 17 publications

(19 citation statements)

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“…Moreover, to compare the obtained estimators with those commonly used in statistics, we determine the MLEs ( q Ψ) of the parameters of the considered covariance structures. Formulae for the MLEs of unknown components of CS and AR(1) can be found in Filipiak et al (2017). Since maximum likelihood estimation of a banded Toeplitz matrix is challenging and no explicit form of MLEs for T 1 and T 2 exist (cf.…”

Section: Resultsmentioning

confidence: 99%

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Covariance regularization for metabolomic data on the drought resistance of barley

Mieldzioc

Mokrzycka

Sawikowska

2019

Biometrical Letters

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SummaryModern 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.

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Section: Resultsmentioning

confidence: 99%

“…For CS and AR(1), the formulae described by Filipiak et al (2017) relating to the separable structure Ψ b Σ (Ψ : pˆp and Σ : qˆq) with q " 1 can also be used.…”

Section: Covariance Regularization Methodsmentioning

confidence: 99%

Covariance regularization for metabolomic data on the drought resistance of barley

Mieldzioc

Mokrzycka

Sawikowska

2019

Biometrical Letters

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“…Complements, clarifications, adjustments, and corrections will continue to be made. The study of Soloveychik and Trushin (2016), which includes a nonrobust analysis section and an algorithm in the robust analysis section, is a superb example of this, and the RST for simple separability (Filipiak et al, 2016(Filipiak et al, , 2017) is a recent breakthrough on the testing side. In closing, most of the estimation and testing procedures discussed here are likelihoodbased and require normal distributions, which are rarely tested in practice.…”

Section: Discussionmentioning

confidence: 99%

“…238-289) and has been largely used with variance-covariance matrices (Muirhead, 1982). By definition, the statistic of the LRT is a ratio of two likelihoods: the maximum (supremum) of the likelihood function under H 0 , divided by the maximum (supremum) of the likelihood function under H. Secondly, Rao's score test (RST; Rao, 1984Rao, , 2005 has been much less used with variance-covariance matrices than the LRT, but may become popular soon in this context (Filipiak et al, 2016(Filipiak et al, , 2017. A complete description of the RST statistic is technical.…”

Section: Preamblementioning

confidence: 99%

Estimation and testing for separable variance–covariance structures

Dutilleul

2018

WIREs Computational Stats

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The statistical analysis of data for a p‐variate response observed repeatedly on q occasions or of spatiotemporal data recorded at p locations by q times for n individuals may require that constraints be imposed on the modeling of the variance–covariance structure of the underlying process, not because of the repeated‐measures or spatiotemporal nature of the data but because there is not enough data otherwise to estimate the model parameters. Besides stationarity and isotropy, separability is an interesting option for that purpose because it reduces the number of variance‐covariance parameters to estimate, from pq(pq + 1)/2 to the Kronecker product of two matrices with p(p + 1)/2 and q(q + 1)/2 parameters. Originally, in the late 1980s, separability of the variance–covariance structure was assumed. Under this model, combined with the normality assumption on the underlying distribution, novel theoretical developments were thus made. The question of estimation of the parameters of a separable variance–covariance structure, more particularly by maximum likelihood, was raised from the early 1990s on, the question of testing for this structure being effectively addressed several years later. The existence and uniqueness of maximum likelihood estimators for the matrix normal distribution (i.e., the doubly multivariate normal distribution characterized by a simply separable variance–covariance structure) have been and remain questions of interest, as shown by recent results. Below, the reader is guided throughout the field of study of the separable variance–covariance structures as the author provides a fair treatment of the topic, its components, extensions (e.g., double separability), and future perspectives. This article is categorized under Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms

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“…The number of repeated measurements p is chosen as 3, 4, 5 and 7, and the number of characteristics q as 3. Filipiak et al [6] showed that the LRT as well as the RST statistics, respectively, do not depend on the choice of and ρ. Nevertheless, in this paper the 3 × 3 variance-covariance matrix is taken as =  2 1 2 1 4 3 2 3 5  and the correlation coefficient ρ of repeated measurements in the CS correlation structure is chosen as 0.5.…”

Section: Observed Type I Error Rates For Biased Lrt and Rst Statisticsmentioning

confidence: 98%

Score test for a separable covariance structure with the first component as compound symmetric correlation matrix

Filipiak

Klein

Roy

2016

Journal of Multivariate Analysis

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a b s t r a c tLikelihood ratio tests (LRTs) for separability of a covariance structure for doubly multivariate data are widely studied in the literature. There are three types of LRT: biased tests based on an asymptotic chi-square null distribution; unbiased/unmodified tests based on an empirical null distribution; and unbiased/modified tests with a test statistic modified to follow a theoretical chi-square null distribution. The Rao's score test (RST) statistic, an alternative for both biased and unbiased/unmodified versions of the corresponding LRT test statistics, is derived for a common case. In this paper the separability of a covariance structure with the first component as a compound symmetric correlation matrix under the assumption of multivariate normality is tested. For this purpose Monte Carlo simulation studies, which compare the biased LRT to biased RST, and unbiased/unmodified LRT to unbiased/unmodified RST, are conducted. It is shown that the RSTs outperform their corresponding LRTs in the sense of empirical Type I error as well as empirical null distribution. Moreover, since the RST does not require estimation of a general variance-covariance matrix (the alternative hypothesis), RST can be performed for small sample sizes, where the variance-covariance matrix could not be estimated for the corresponding LRT, making the LRT infeasible. Three examples are presented to illustrate and compare statistical inference based on LRT and RST.

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A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures

Cited by 17 publications

References 25 publications

Covariance regularization for metabolomic data on the drought resistance of barley

Covariance regularization for metabolomic data on the drought resistance of barley

Estimation and testing for separable variance–covariance structures

Score test for a separable covariance structure with the first component as compound symmetric correlation matrix

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