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MULTIPLE OUTLIER DETECTION IN GROWTH CURVE MODEL

WITH UNSTRUCTURED COVARIANCE MATRIX

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JIAN-XIN PAN^{ 1} AND
KAI-TAI FANG^{ 2}

^{1} *Department of Mathematics, Hong Kong Baptist University,*

224 Waterloo Road, Kowloon, Hong Kong

and Department of Statistics, Yunnan University, Kunming
650091,
China

^{2} *Department of Mathematics, Hong Kong Baptist University,*

224 Waterloo Road, Kowloon, Hong Kong

and Institute of Applied Mathematics, Academia Sinica,
Beijing
100080, China
(Received January 31, 1994; revised June 21, 1994)

**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.

*Key words and phrases*:
Elliptically contoured
distribution, growth curve
model, influential observation, multiple
outlier detection criterion, statistical diagnostic.

**Source**
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