Estimation of regression coefficients in case of differentiable error processes

Abstract

Consider the problem of estimating the coefficient β in the regression model where the regression function f is similar to the covariance kernel R of the error process N, i.e., f is an element of the reproducing kernel Hilbert space associated with R. Conventional approaches discuss asymptotically optimal estimators if the kernel satisfies certain regularity conditions and if f is expressible as the image of R under an appropriate linear transformation. This paper introduces estimators which are based on direct approximations of the (nonobservable) best linear unbiased estimator of β. Regularity conditions are not required, the representation of f may also depend on derivatives of R, and particular emphasis is laid on computational stability.