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2004-25

A Note on Designs for Estimating Population Parameters

by Entholzner, M., Benda, N., Schmelter, Th., Schwabe, R..


Series: 2004-25, Preprints

MSC:
62K05 Optimal designs
62J10 Analysis of variance and covariance
62H12 Estimation
62P10 Applications to biology and medical sciences

Abstract:
In various fields, data from repeated measurements are
pooled across individuals to obtain valid estimates for
population characteristics. If the individual effects are
treated as random, mixed models can be fitted to the data.
In the case that the same design is used for all
individuals, the ordinary and the weighted least squares
estimator both coincide with the average of
individually fitted curves. In this situation optimal and
efficient designs can be obtained.
The results are extended to situations where
different treatments are compared.

Keywords:
otimal design, mixed model, weighted least squares, population parameters, repeated measurements, random regression, random coefficient regression, hierarchical model, growth curves, treatment comparisons