Estimation and Testing Hypotheses in Two-Level and Three-Level Multivariate Data with Block Compound Symmetric Covariance Structure

Arkadiusz Kozioł, Anuradha Roy*, Roman Zmyślony, Ivan Žežula, Miguel Fonseca

*Bijbehorende auteur voor dit werk

OnderzoeksoutputAcademicpeer review


This article deals with the estimation and hypotheses testing problems for two-level and three-level multivariate data. The coordinate-free approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices for both two-level and three-level multivariate data. The estimators are shown to be unbiased, sufficient, complete, and consistent. A competitor for the likelihood ratio test on covariance components under linear constraints and the mean vectors are proposed, based on the F distribution. Simulation studies are conducted to see the power of the proposed tests and the proposed methods are implemented with two medical datasets.
Originele taal-2English
TitelMultivariate, Multilinear and Mixed Linear Models
RedacteurenKatarzyna Filipiak, Augustyn Markiewicz, Dietrich von Rosen
Plaats van productieCham
ISBN van elektronische versie978-3-030-75494-5
ISBN van geprinte versie978-3-030-75496-9, 978-3-030-75493-8
StatusPublished - 2-okt.-2021
Extern gepubliceerdJa

Publicatie series

NaamContributions to Statistics
ISSN van geprinte versie1431-1968

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