MSE’S OF PREDICTION IN GROWTH CURVE MODEL WITH COVARIANCE STRUCTURES

T. KANDA

Department of Mathematics, Hiroshima Institute of Technology, Miyake, Saeki-ku, Hiroshima 731-51, Japan

(Received January 21, 1991; revised October 30, 1991)

Abstract. We consider the growth curve model with covariance structures: positive-definite, uniform covariance structure and serial covariance structure. Two types of prediction problems are studied in this paper. One is called the conditional prediction problem and the other is called the extended prediction problem. For both types of prediction problems, the mean squared error for a serial covariance structure is obtained for the estimates based on the conditional expectation; the mean squared error for an unrestricted covariance structure is compared with the mean squared error for a uniform covariance structure or a serial covariance structure. These results are exemplified by two sets of real data.

Key words and phrases: Growth curve model, serial covariance structure, uniform covariance structure, mean squared error, conditional prediction, extended prediction.