Asymptotic Optimality of Regular Sequence Designs
نویسنده
چکیده
We study linear estimators for the weighted integral of a stochastic process. The process may only be observed on a nite sampling design. The error is deened in mean square sense, and the process is assumed to satisfy Sacks-Ylvisaker regularity conditions of order r 2 N 0. We show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators. Hereby we extend results by Sacks and Ylvisaker for regularity r = 0 or 1, and we connrm a conjecture by Eubank, Smith, and Smith.
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