Computations of Optimal Experimental Designs of Estimation of Linear Forms.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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Suppose that for each point s of a compact metric space S an experiment can be performed whose outcome is a random variable ys, the variance of ys being independent of s and the mean of ys being of the form theta, fs summation from 1 to N theta j fjs. The fjs are the linearly independent continuous regression functions and the theta js are the unknown regression coefficients. The experimenter plans to make N uncorrelated observations ys1,...,ysN in order to estimate a linear form c, theta summation from 1 to N of cj theta j, where c c1,...,cn is a given nonzero vector. The experimental designs which are optimal for the estimation of c, theta have been characterized in an elegant geometric manner by Elfving 1952 and Karlin and Studden 1966a. It is shown here that, in conjunction with the methods of mathematical programming, this characterization leads to effective procedures for the computation of optimal designs whenever S is finite and of nearly optimal designs when S is infinite and the regression functions are Lipschitzian. Author
- Statistics and Probability
- Operations Research