Ratio F test for testing simultaneous hypotheses in models with blocked compound symmetric covariance structure

This article deals with testing simultaneous hypotheses about the mean structure and the covariance structure in models with blocked compound symmetric (BCS) covariance structure. Considered models are used for double multivariate data, which means that m -variate vector of observation is measured r...

Full description

Saved in:
Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Vol. 62; no. 5; pp. 2109 - 2118
Main Authors: Zmyślony, Roman, Kozioł, Arkadiusz
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
Springer Nature B.V
Subjects:
Covariance matrix
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Hypotheses
Insurance
Management
Mathematical analysis
Mathematics and Statistics
Mean
Multivariate analysis
Normality
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Research Article
Statistical tests
Statistics
Statistics for Business
Structure of mean vector
Structure of covariance matrices
Positive and negative part of estimator
Best unbiased estimator
Block compound symmetric covariance structure
Double multivariate data
Testing hypotheses
ISSN:0932-5026, 1613-9798
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article deals with testing simultaneous hypotheses about the mean structure and the covariance structure in models with blocked compound symmetric (BCS) covariance structure. Considered models are used for double multivariate data, which means that m -variate vector of observation is measured repeatedly over u levels of some factor on each of n individual. Additionally, the assumption of multivariate normality for this type of data is made. We use framework of ratio of positive and negative parts of best unbiased estimators to obtain simultaneous F test. The test statistic is constructed as a ratio of test statistics for testing single hypotheses about the mean vector and the covariance matrix. In simulation study power of obtained test is compared with powers of three other F tests—two for testing single hypotheses and one for testing simultaneous hypotheses, whose test statistic is convex combination of test statistics of these two single F tests. The problem of simultaneous testing of the mean vector and covariance matrix was also consider in paper (Hyodo and Nishiyama, Commun Stat Theory Methods, https://doi.org/10.1080/03610926.2019.1639751 , 2019).
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-020-01182-4