SAMPLING DESIGNS FOR REGRESSION COEFFICIENT ESTIMATION WITH CORRELATED ERRORS

YINGCAI SU^{1} AND STAMATIS CAMBANIS^{2}

1Department of Statistics, University of Arizona, Tucson, AZ 85721, U.S.A. 2Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, U.S.A.

(Received March 1, 1993; revised December 9, 1993)

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.

Key words and phrases: Regression coefficient estimation, sampling designs, correlated errors.