We develop a variance reduction method for smoothing splines. We do this by showing that the quadratic interpolation method introduced in Cheng et al. (2006), for local linear estimators, also works for smoothing splines. For a given point of estimation, Cheng et al. (2006) define a variance-reduced local linear estimate as a linear combination of classical estimates at three nearby points. We ...

In this paper a new smooth backfitting estimate is proposed for additive regression models. The estimate has the simple structure of Nadaraya–Watson smooth backfitting but at the same time achieves the oracle property of local linear smooth backfitting. Each component is estimated with the same asymptotic accuracy as if the other components were known. 1. Introduction. In additive models it is ...

For the solution of large, sparse, non-Hermitian linear systems, Lanczos-type product methods that are based on the Lanczos three-term recurrence are derived in a systematic way. These methods either square the Lanczos process or combine it with a local minimization of the residual. For them a quasi-minimal residual (QMR) smoothing is proposed that can also be implemented by short-term recurren...

This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the Lagrangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the crossvalidation procedure for selecting the o...

There recently has been much interest in non-interior continuation/smoothing methods for solving linear/nonlinear complementarity problems. We describe extensions of such methods to complementarity problems defined over the cone of block-diagonal symmetric positive semidefinite real matrices. These extensions involve the Chen-Mangasarian class of smoothing functions and the smoothed Fischer-Bur...

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/ √ n. Asymptotic critical values ...

The problem of constructing and approximating control theoretic smoothing splines is considered in this paper. It is shown that the optimal approximating function can be given as the solution of a forced Hamiltonian system, that can be explicitly solved using the Riccati transform, and an explicit linear filter can be constructed. We show that the bandwidth of the filter can be naturally contro...