Open Access
Translator Disclaimer
August 2017 A new approach to optimal designs for correlated observations
Holger Dette, Maria Konstantinou, Anatoly Zhigljavsky
Ann. Statist. 45(4): 1579-1608 (August 2017). DOI: 10.1214/16-AOS1500

Abstract

This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of observations and considers the asymptotic properties of estimators and designs as the sample size converges to infinity, our approach is based on a continuous time model. We use results from stochastic analysis to identify the best linear unbiased estimator (BLUE) in this model. Based on the BLUE, we construct an efficient linear estimator and corresponding optimal designs in the model for finite sample size by minimizing the mean squared error between the optimal solution in the continuous time model and its discrete approximation with respect to the weights (of the linear estimator) and the optimal design points, in particular in the multiparameter case.

In contrast to previous work on the subject, the resulting estimators and corresponding optimal designs are very efficient and easy to implement. This means that they are practically not distinguishable from the weighted least squares estimator and the corresponding optimal designs, which have to be found numerically by nonconvex discrete optimization. The advantages of the new approach are illustrated in several numerical examples.

Citation

Download Citation

Holger Dette. Maria Konstantinou. Anatoly Zhigljavsky. "A new approach to optimal designs for correlated observations." Ann. Statist. 45 (4) 1579 - 1608, August 2017. https://doi.org/10.1214/16-AOS1500

Information

Received: 1 November 2015; Revised: 1 June 2016; Published: August 2017
First available in Project Euclid: 28 June 2017

zbMATH: 06773284
MathSciNet: MR3670189
Digital Object Identifier: 10.1214/16-AOS1500

Subjects:
Primary: 62K05
Secondary: 62M05

Keywords: correlated observations , Doob representation , Gaussian white mouse model , Linear regression , optimal design , quadrature formulas

Rights: Copyright © 2017 Institute of Mathematical Statistics

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.45 • No. 4 • August 2017
Back to Top