SpatCorrNPR
Local polynomial regression is a widely used smoothing method in nonparametric statistics, and the main tuning parameter of this method is the bandwidth, which is susceptible to correlation. Several techniques exist for bandwidth selection with uncorrelated errors and even fewer for the correlated errors scenario; however, the availability of these implementations is meager and, in some cases, nonexistent. To address this gap, we present a new MATLAB and Octave toolbox called SpatCorrNPR under Windows and Linux for local polynomial regression estimation with correlated errors. The SpatCorrNPR toolbox supports one and two-dimensional regression problems with several bandwidth selection methods designed to combat the effects of correlation. Additionally, SpatCorrNPR provides covariance estimation capabilities, such as building semivariograms and performing geoplotting for spatial datasets. This toolbox can be accessed in three forms: a MATLAB graphical user interface (GUI), a MATLAB command line toolbox, and an Octave toolbox. The toolbox is written in MATLAB to take advantage of the efficient computing system, and the Octave counterpart increases its availability to the user. We also demonstrate the utility of this toolbox with an illustrative example, and further compare the proposed toolbox to other software implementations using some practical datasets.
M. Tabassum & K. De Brabanter, SpatCorrNPR: A MATLAB/Octave toolbox for Local Polynomial Regression with Correlated Errors, 2025. (article will be made available soon!)
fourierin
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
StatLSSVM
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/)