We introduce a new nonparametric regression estimator that uses prior information on regression shape in the form of a parametric model. In eeect, we nonparametrically encompass the parametric model. We obtain estimates of the regression function and its derivatives along with local parameter estimates that can be interpreted from within the parametric model. We establish the uniform consistenc...

The ordinary least squares estimation is based on minimization of the squared distance of the response variable to its conditional mean given the predictor variable. We extend this method by including in the criterion function the distance of the squared response variable to its second conditional moment. It is shown that this “second-order” least squares estimator is asymptotically more effici...

We consider the fixed interval smoothing problem for data from linear or nonlinear models where there is a priori information about the boundary values of the state process. The nonlinearities and boundary values preclude a stochastic approach so instead we use a least squares methodology. The resulting variational equations are a coupled system of ordinary differential equations for the state ...

The consistency and asymptotic normality of a linear least squares estimate of the form (X,X)-X’Y when the mean is not X/I is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not ...