On the sequential construction of optimum bounded designs

We consider a parameter estimation problem with independent observations where one samples from a finite population of independent and identically distributed experimental conditions X. The size of the population is N but only n samples, a proportion α of N , can be used. The quality of a sample is measured by a regular optimality criterion φ(·) based on the information matrix, such as the D-criterion. The construction of an optimal approximate design bounded by μ/α, with μ the probability measure of X, can be used to construct a sampling strategy which is asymptotically optimum (when the size N of the population tends to infinity). We show that a sequential strategy which does not require any information on μ is also asymptotically optimum. Some possible applications are indicated.