Sampling designs for regression coefficient estimation with correlated errors

Abstract

The problem of estimating regression coefficients from observations at a finite number of properly designed sampling points is considered when the error process has correlated values and no quadratic mean derivative. Sacks and Ylvisaker (1966, Ann. Math. Statist., 39, 66-89) found an asymptotically optimal design for the best linear unbiased estimator (BLUE). Here, the goal is to find an asymptotically optimal design for a simpler estimator. This is achieved by properly adjusting the median sampling design and the simpler estimator introduced by Schoenfelder (1978, Institute of Statistics Mimeo Series No. 1201, University of North Carolina, Chapel Hill). Examples with stationary (Gauss-Markov) and nonstationary (Wiener) error processes and with linear and nonlinear regression functions are considered both analytically and numerically.

Document Type

Article

DOI

https://doi.org/10.1007/BF00773477

Keywords

correlated errors, Regression coefficient estimation, sampling designs

Publication Date

12-1-1994

Journal Title

Annals of the Institute of Statistical Mathematics

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