In classical smoothing splines, the smoothness is controlled by a single smoothing parameter that penalizes the roughness uniformly across the whole domain. Adaptive smoothing splines extend this framework to allow the smoothing parameter to change in the domain, adapting to the change of roughness. In this article we propose a data driven method to nonparametrically model the penalty function....

Noncausal estimation algorithms, which involve smoothing, can be used for off-line identification of nonstationary systems. Since smoothing is based on both past and future data, it offers increased accuracy compared to causal (tracking) estimation schemes, incorporating past data only. It is shown that efficient smoothing variants of the popular exponentially weighted least squares and Kalman ...

In industries, how to improve forecasting accuracy such as sales, shipping is an important issue. There are many researches made on this. In this paper, a hybrid method is introduced and plural methods are compared. Focusing that the equation of exponential smoothing method(ESM) is equivalent to (1,1) order ARMA model equation, new method of estimation of smoothing constant in exponential smoot...

We discuss the l2-lp (with p ∈ (0, 1)) matrix minimization for recovering low rank matrix. A smoothing approach is developed for solving this non-smooth, non-Lipschitz and non-convex optimization problem, in which the smoothing parameter is used as a variable and a majorization method is adopted to solve the smoothing problem. The convergence theorem shows that any accumulation point of the seq...

A method of counts-in-cells analysis of galaxy distribution is investigated with arbitrary smoothing functions in obtaining the galaxy counts. We explore the possiblity of optimizing the smoothing function, considering a series of m-weight Epanechnikov kernels. The popular top-hat and Gaussian smoothing functions are two special cases in this series. In this paper, we mainly consider the second...

In kernel discriminant analysis, it is common practice to select the smoothing parameter (bandwidth) based on the training data and use it for classifying all unlabeled observations. But this method of selecting a single scale of smoothing ignores the major issue of model uncertainty. Moreover, in addition to depending on the training sample, a good choice of bandwidth may also depend on the ob...

This paper has a focus on non-stationary time series formed from small non-negative integer values which may contain many zeros and may be over-dispersed. It describes a study undertaken to compare various suitable adaptations of the simple exponential smoothing method of forecasting on a database of demand series for slow moving car parts. The methods considered include simple exponential smoo...

We consider ®rst the spline smoothing nonparametric estimation with variable smoothing parameter and arbitrary design density function and show that the corresponding equivalent kernel can be approximated by the Green function of a certain linear differential operator. Furthermore, we propose to use the standard (in applied mathematics and engineering) method for asymptotic solution of linear d...

A multiscale morphological dilation-erosion smoothing operation and its associated scale-space expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scale-space monotonic property for signal extrema is demonstrated. Scale-space ngerprints from this approach have advantages over Gaussian scale-space ngerprints in that they:...