APPROXIMATING THE MEAN SQUARED PREDICTION ERROR IN LINEAR-MODELS UNDER THE FAMILY OF EXPONENTIAL CORRELATIONS

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