MULTIPLE OUTLIER DETECTION IN GROWTH CURVE MODEL WITH UNSTRUCTURED COVARIANCE MATRIX

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

1Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon, Hong Kong and Department of Statistics, Yunnan University, Kunming 650091, China 2Department 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.