Open Access
February 2013 Optimal design for linear models with correlated observations
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
Ann. Statist. 41(1): 143-176 (February 2013). DOI: 10.1214/12-AOS1079


In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is provided, which extends the classical equivalence theory for optimal designs in models with uncorrelated errors to the case of dependent data. If the regression functions are eigenfunctions of an integral operator defined by the covariance kernel, it is shown that the corresponding measure defines a universally optimal design. For several models universally optimal designs can be identified explicitly. In particular, it is proved that the uniform distribution is universally optimal for a class of trigonometric regression models with a broad class of covariance kernels and that the arcsine distribution is universally optimal for the polynomial regression model with correlation structure defined by the logarithmic potential. To the best knowledge of the authors these findings provide the first explicit results on optimal designs for regression models with correlated observations, which are not restricted to the location scale model.


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Holger Dette. Andrey Pepelyshev. Anatoly Zhigljavsky. "Optimal design for linear models with correlated observations." Ann. Statist. 41 (1) 143 - 176, February 2013.


Published: February 2013
First available in Project Euclid: 5 March 2013

zbMATH: 1347.62161
MathSciNet: MR3059413
Digital Object Identifier: 10.1214/12-AOS1079

Primary: 60G10 , 62K05
Secondary: 31A10 , 45C05‎

Keywords: arcsine distribution , correlated observations , Eigenfunctions , ‎integral operator , Logarithmic potential , optimal design

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 1 • February 2013
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