The Annals of Statistics

Some Model Robust Designs in Regression

Jerome Sacks and Donald Ylvisaker

Full-text: Open access

Abstract

Theory for finding designs in estimating a linear functional of a regression function is developed for classes of regression functions which are infinite dimensional. These classes can be viewed as representing possible departures from an "ideal" simple model and thus describe a model robust setting. The estimates are restricted to be linear and the design (and estimate) sought is minimax for mean square error. The structure of the design is obtained in a variety of cases; some asymptotic theory is given when the functionals are integrals. As to be expected, optimal designs depend critically on the particular functional to be estimated. The associated estimate is generally not a least squares estimate but we note some examples where a least squares estimate, in conjunction with a good design, is adequate.

Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1324-1348.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346795

Digital Object Identifier
doi:10.1214/aos/1176346795

Mathematical Reviews number (MathSciNet)
MR760692

Zentralblatt MATH identifier
0556.62054

JSTOR
links.jstor.org

Subjects
Primary: 62K05: Optimal designs
Secondary: 62J02: General nonlinear regression

Keywords
Optimal design model robustness regression design approximately linear models nonparametric regression linear estimation minimax designs

Citation

Sacks, Jerome; Ylvisaker, Donald. Some Model Robust Designs in Regression. Ann. Statist. 12 (1984), no. 4, 1324--1348. doi:10.1214/aos/1176346795. https://projecteuclid.org/euclid.aos/1176346795


Export citation