It is widely known that, in a certain sense, a smoothing spline estimate of the regression function is asymptotically equivalent to a kernel regression estimate. However, little information has been available about the equivalence between nonparametric regression tests, based on the smoothing spline and local polynomial regression methods. To assess their relative behaviors and to facilitate il...

In this paper, we propose a Big-? smoothing method for solving the P 0 matrix linear complementarity problem. We study the trajectory deened by the augmented smoothing equations and global convergence of the method under an assumption that the original P 0 matrix linear complementarity problem has a solution. The method has been tested on the P 0 matrix linear complementarity problem with unbou...

There recently has been much interest in non-interior continuation/smoothingmethods 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 ChenMangasarian class of smoothing functions and the smoothed Fischer-Burme...

We present a method for smoothing discontinuous dynamics involving contact and friction, thereby facilitating the use of local optimization techniques for control. The method replaces the standard Linear Complementarity Problem with a Stochastic Linear Complementarity Problem. The resulting dynamics are continuously differentiable, and the resulting controllers are robust to disturbances. We de...

A method that utilizes embedded geometric structure is proposed, to enhance clustering. The geometric structure is identified via a combination of a local smoothing method – local linear projection (LLP) – and a computational method for the geodesic distance. It is found that comparing to existing algorithms, it is more efficient to deal with noisy and “structured” data. Simulations for both sy...

SIMEX methods are attractive for solving curve estimation problems in errors-in-variables regression, using parametric or semiparametric techniques. However, nonparametric approaches are generally of quite a different type, being based on, for example, kernels, local-linear modeling, ridging, orthogonal series, or splines. All of these techniques involve the challenging (and not well studied) i...

We study evolution of various statistical quantities of smoothed cosmic density and velocity fields using N-body simulations. The parameter C ≡ 〈V 2δ〉 /(〈V 2〉 〈δ2〉) characterizes nonlinear coupling of these two fields and determines behavior of bulk velocity dispersion as a function of local density contrast. It is found that this parameter depends strongly on the smoothing scale even in quasi-...

We consider fully discrete schemes for the one dimensional linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model are presented in these approximations. In particular Strichartz estimates and the local smoothing of the numerical solutions are analyzed. Using a backward Euler approximation of the linear semigroup we introduce a convergent sche...