Many popular curve estimators based on smoothing have diicul-ties caused by boundary eeects. These eeects are visually disturbing in practice and can play a dominant role in theoretical analysis. Local polynomial regression smoothers are known to correct boundary eeects automatically. Some analogs are implemented for density estimation and the resulting estimators also achieve automatic boundar...

Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted averaging, at the price of high computational cost. In this paper, we introduce a highly efficient splitting-based method for global EPS that minimizes the o...

Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (1978,1983) showed that smoothing splines are also Bayes estimates and used the corresponding prior model to derive interval estimates for the regression function. Although the interval estimates work well on a global basis, they can have poor local properties. The source of this problem is the use of a ...

This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In proposed method, we apply TME method to approximate transition density of stochastic differential equation in dynamic model. Furthermore, derive a theoretical error bound (in mean square sense) estimates showing that smoother stable under weak assumptions. ...

It is known that a surface fitted by conventional local smoothing procedures is not statistically consistent at the jump locations of the true regression surface. In this paper, a procedure is suggested for modifying conventional local smoothing procedures such that the modified procedures can fit the surface with jumps preserved automatically. Taking the local linear kernel smoothing procedure...

We present skeleton studies of non-Gaussianity in the cosmic microwave background temperature anisotropy observed in the 5-yr Wilkinson Microwave Anisotropy Probe (WMAP) data. The local skeleton is traced on the 2D sphere by cubic spline interpolation which leads to more accurate estimation of the intersection positions between the skeleton and the secondary pixels than conventional linear inte...