Multiple outlier detection in growth curve model with unstructured covariance matrix |
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Authors: | Jian-Xin Pan Kai-Tai Fang |
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Institution: | (1) Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon, Hong Kong, China;(2) Department of Statistics, Yunnan University, 650091 Kunming, China;(3) Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon, Hong Kong, China;(4) Institute of Applied Mathematics, Academia Sinica, 100080 Beijing, China |
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Abstract: | Under a normal assumption, Liski (1991,Biometrics,47, 659–668) gave some measurements for assessing influential observations in a Growth Curve Model (GCM) with a known covariance. For the GCM with an arbitrary (p.d.) covariance structure, known as unstructured covariance matrix (UCM), the problems of detecting multiple outliers are discussed in this paper. When a multivariate normal error is assumed, the MLEs of the parameters in the Multiple-Individual-Deletion model (MIDM) and the Mean-Shift-Regression model (MSRM) are derived, respectively. In order to detect multiple outliers in the GCM with UCM, the likelihood ratio testing statistic in MSRM is established and its null distribution is derived. For illustration, two numerical examples are discussed, which shows that the criteria presented in this paper are useful in practice.Supported partially by the WAI TAK Investment and Loan Company Ltd. Research Scholarship of Hong Kong for 1992–93.Supported partially by the Hong Kong UPGC Grant. |
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Keywords: | Elliptically contoured distribution growth curve model influential observation multiple outlier detection criterion statistical diagnostic |
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