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Testing Sphericity and Intraclass Covariance Structures under a Growth Curve Model in High Dimension
University of Toronto, Department of Statistics.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-9896-4438
2016 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141Article in journal (Refereed) Accepted
Abstract [en]

In this paper we consider the problem of testing (a) sphericity and (b) intraclass covariance structure under a Growth Curve model. The maximum likelihood estimator (MLE) for the mean in a Growth Curve model is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N. The MLE for the covariance matrix is based on the MLE for the mean, which can be very poor for p close to N. For both structures (a) and (b), we modify the MLE for the mean to an unweighted estimator and based on this estimator we propose a new estimator for the covariance matrix. This new estimator leads to new tests for (a) and (b). We also propose two other tests for each structure, which are just based on the sample covariance matrix.

To compare the performance of all four tests we compute for each structure (a) and (b) the attained significance level and the empirical power. We show that one of the tests based on the sample covariance matrix is better than the likelihood ratio test based on the MLE. 

Place, publisher, year, edition, pages
2016.
Keyword [en]
Growth Curve model; GMANOVA; Sphericity; Intraclass co- variance structure; Hypothesis testing; Asymptotic distribution; Power com- parison; High dimension
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-126956OAI: oai:DiVA.org:liu-126956DiVA: diva2:918060
Available from: 2016-04-08 Created: 2016-04-08 Last updated: 2016-04-25

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Singull, Martin
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Mathematical Statistics Faculty of Science & Engineering
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