## The Annals of Statistics

### Asymptotic optimality of regular sequence designs

Klaus Ritter

#### Abstract

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

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

Dates
First available in Project Euclid: 20 November 2003

https://projecteuclid.org/euclid.aos/1069362311

Digital Object Identifier
doi:10.1214/aos/1069362311

Mathematical Reviews number (MathSciNet)
MR1421162

Zentralblatt MATH identifier
0905.62077

#### Citation

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