ASYMPTOTIC OPTIMALITY OF REGULAR SEQUENCE DESIGNS

We study linear estimators for the weighted integral of a stochastic p rocess. The process may only be observed on a finite sampling design. The error is defined in a mean square sense, and the process is assume d to satisfy Sacks-Ylvisaker regularity conditions of order r is an el ement of N-0. We show that sampling at the quantiles of a particular d ensity already yields asymptotically optimal estimators. Hereby we ext end the results of Sacks and Ylvisaker for regularity r = 0 or 1, and we confirm a conjecture by Eubank, Smith and Smith.