Computations of Optimal Experimental Designs of Estimation of Linear Forms.

摘要

Suppose that for each point s of a compact metric space S an experiment can be performed whose outcome is a random variable y(s),the variance of y(s) being independent of s and the mean of y(s) being of the form summation from 1to N (theta j) fj(s). The fj's are the linearly independent continuous regression functions and the theta j's are the unknown regression coefficients. The experimenter plans to make N uncorrelated observations y(s1),...,y(sN) in order to estimate a linear form < c,theta > =summation from 1to 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)