The R package fourierin for evaluating functions defined as Fourier-type integrals over a collection of argument values. The integrals are finitely supported with integrands involving continuous functions of one or two variables. As an important application, such Fourier integrals arise in so-called “inversion formulas”, where one seeks to evaluate a probability density at a series of points from a given characteristic function (or vice versa) through Fourier transforms. This paper intends to fill a gap in current R software, where tools for repeated evaluation of functions as Fourier integrals are not directly available. We implement two approaches for such computations with numerical integration. In particular, if the argument collection for evaluation corresponds to a regular grid, then an algorithm from Inverarity (2002) may be employed based on a fast Fourier transform, which creates significant improvements in the speed over a second approach to numerical Fourier integration (where the latter also applies to cases where the points for evaluation are not on a grid).
G. Basulto-Elias, A. Carriquiry, K. De Brabanter and D.J. Nordman, ``fourierin'': An R package to compute Fourier integrals, R Journal, vol. 9, no. 2, 72-83, 2017
This a free available Matlab (R2009b and higher) toolbox under Windows, Linux and Mac for nonparametric regression estimation based on least squares support vector machines (LS-SVM) called StatLSSVM which is short for statistical library for least squares support vector machines. StatLSSVM facilitates use of simple Matlab syntax and inherits its fast matrix-matrix and matrix-vector multiplications. The toolbox is written so that only a few lines of code are necessary in order to perform standard nonparametric regression, regression with correlated errors, robust regression and univariate and bivariate density estimation. In addition, construction of additive models and pointwise or uniform confidence intervals are also supported. A number of tuning criteria such as classical cross-validation, robust cross-validation, cross-validation for correlated errors and least squares cross validation for histogram binwidth tuning are available to the user. Also, minimization of the previous criteria is available without any user interaction.
The StatLSSVM toolbox aims at offering the statistician an easy and fully functional set of nonparametric regression tools based on LS-SVM.
Kris De Brabanter, Johan A. K. Suykens, Bart De Moor (2013). Nonparametric Regression via StatLSSVM. Journal of Statistical Software, 55(2), 1-21. (JSS link http://www.jstatsoft.org/v55/i02/)