The archetypal Savitzky–Golay convolutional filter matches a polynomial to even-spaced data and uses this to measure smoothed derivatives. We synthesize a scheme in which heterogeneous, anisotropic linearly separable basis functions combine to provide a general smoothing, derivative measurement and reconsruction function for point coulds in multiple dimensions using a linear operator in the for...

This paper introduces the R package FKSUM, which offers fast and exact evaluation of univariate kernel smoothers. The main computations are implemented in C++, wrapped simple, intuitive versatile functions. based on recursive expressions involving order statistics, allows for smoothers at all sample points log-linear time. In addition to general purpose smoothing functions, built readyto-use im...

In this paper we present a unified discussion of different approaches to the identification of smoothing spline analysis of variance (ANOVA) models: (i) the “classical” approach (in the line of Wahba in Spline Models for Observational Data, 1990; Gu in Smoothing Spline ANOVA Models, 2002; Storlie et al. in Stat. Sin., 2011) and (ii) the State-Dependent Regression (SDR) approach of Young in Nonl...

This paper develops a robust testing procedure for the nonparametric kernel method in the presence of temporal dependence of unknown forms. We …rst propose a new variance estimator that corrects the …nite sample bias caused by temporal dependence. The new variance estimator is novel in the sense that it is not only robust to temporal dependence in …nite samples but also consistent in large samp...

Traditional kernel methods for estimating the spatially-varying density of points in a spatial point pattern may exhibit unrealistic artefacts, addition to familiar problems bias and over- or under-smoothing. Performance can be improved by using diffusion smoothing, which smoothing is heat on domain. This paper develops into practical statistical methodology two-dimensional data. We clarify adv...

This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number of potential future scenarios. Instead of starting a separate nested Monte Carlo simulation for each scenario under consideration, the new method covers the u...