Testing Some Covariance Structures under a Growth Curve Model in High Dimension

• fIn 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. or both structures (a) and (b), we modify the MLE for the mean to n 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 or each structure (a) and (b) the attained signicance 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Growth Curve model; GMANOVA; Sphericity; Intraclass covariance structure; Hypothesis testing; Asymptotic distribution; Power comparison; High dimension

Publikations- och innehållstyp

vet (ämneskategori)

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