Prediction of Future Observations in Polynomial Growth Curve Models. Part 1.
PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
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The problem considered is that of simultaneous prediction of future measurements on a given number of individuals using their past measurements. Assuming a polynomial growth curve model, a number of methods are proposed and their relative efficiencies in terms of the compound mean square prediction error CMPSE are compared. There is a similarity between the problem of simultaneous estimation of parameters as considered by Stein and that of simultaneous prediction of future observations. It is found that the empirical Bayes predictor EBP based on the empirical Bayes estimator EBE of the unknown vector parameters in several linear models proposed by the author Rao, 1975 has the best possible efficiency compared to the others studied. The problem of determining the appropriate degree of the polynomial growth curve is also studied from the point of view of minimising the CMSPE. Author
- Statistics and Probability