The Annals of Statistics

Asymptotic optimality of regular sequence designs

Klaus Ritter

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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 $r \epsilon \mathbb{N}_0$. 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.

Article information

Ann. Statist., Volume 24, Number 5 (1996), 2081-2096.

First available in Project Euclid: 20 November 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs 41A55: Approximate quadratures
Secondary: 60G12: General second-order processes 62M99: None of the above, but in this section 65D30: Numerical integration

Integral estimation asymptotically optimal designs regular sequence designs Sacks-Ylvisaker conditions


Ritter, Klaus. Asymptotic optimality of regular sequence designs. Ann. Statist. 24 (1996), no. 5, 2081--2096. doi:10.1214/aos/1069362311.

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