SAMPLING DESIGNS FOR REGRESSION COEFFICIENT ESTIMATION WITH CORRELATED ERRORS

The problem of estimating regression coefficients from observations at a finite number of properly designed sampling points is considered wh en the error process has correlated values and no quadratic mean deriv ative. Sacks and Ylvisaker (1966, Ann. Math. Statist., 39, 66-89) foun d an asymptotically optimal design for the best linear unbiased estima tor (BLUE). Here, the goal is to find an asymptotically optimal design for a simpler estimator. This is achieved by properly adjusting the m edian sampling design and the simpler estimator introduced by Schoenfe lder (1978, Institute of Statistics Mimeo Series No. 1201, University of North Carolina, Chapel Hill), Examples with stationary (Gauss-Marko v) and nonstationary (Wiener) error processes and with linear and nonl inear regression functions are considered both analytically and numeri cally.