Statistica Sinica 8(1998), 511-526

APPROXIMATING THE MEAN SQUARED PREDICTION

ERROR IN LINEAR MODELS UNDER THE FAMILY OF

EXPONENTIAL CORRELATIONS

Markus Abt

University of Waterloo

Abstract: We investigate approximations for the mean squared prediction error in a linear regression model with correlated errors. The correlation structure is assumed to be the family of exponential correlations widely used in practical applications of computer experiments. Well known members of this family include the Ornstein-Uhlenbeck process as well as stochastic processes with analytic sample paths. Special emphasis is put on the situation when the true values of the parameters involved in the correlation structure are on the boundary of the parameter space.

Key words and phrases: Fisher information matrix, Gaussian stochastic processes, homogeneous random fields, mean squared prediction error.