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Test for the mean matrix in a Growth Curve model for high dimensions
Department of Statistics, University of Toronto, 100 St. George Street, Toronto, Canada, M5S 3G3.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-9896-4438
2014 (English)Report (Other academic)
Place, publisher, year, edition, pages
Linköping University Electronic Press, 2014. , 23 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2014:13
Keyword [en]
Asymptotic distribution; High dimension; GMANOVA; Growth Curve Model; Estimation; Hypothesis testing; Power comparison.
National Category
URN: urn:nbn:se:liu:diva-111530ISRN: LiTH-MAT-R--2014/13--SEOAI: diva2:757377

In this paper, we consider the problem of estimating and testing a general linear hypothesis in a general multivariate linear model, the so called Growth Curve model, when the pN observation matrix is normally distributed with an unknown covariance matrix.

   The maximum likelihood estimator (MLE) for the mean 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. We modify the MLE to an unweighted estimator and propose a new test which we compare with the previous likelihood ratio test (LRT) based on the weighted estimator, i.e., the MLE. We show that the performance of this new test based on the unweighted estimator is better than the LRT based on the MLE.

   For the high-dimensional case, when p is larger than N, we construct two new tests based on the trace of the variation matrices due to the hypothesis (between sum of squares) and the error (within sum of squares).   To compare the performance of all four tests we compute the attained signicance level and the empirical power.

Available from: 2014-10-22 Created: 2014-10-22 Last updated: 2014-10-22

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Singull, Martin
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