Asymptotic optimality of regular sequence designs

• 成果类型: Article
• 署名作者: Ritter, K
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1069362311
• 发表日期: 1996
• 页码: 2081-2096
• 关键词: average-case complexity; isotropic wiener measure; STOCHASTIC-PROCESSES; multivariate integration; sampling designs; approximation; regression; models

摘要

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