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We present the R package fourierin (Basulto-Elias, 2017) 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). We illustrate the package with the computation of probability densities and characteristic functions through Fourier integrals/transforms, for both univariate and bivariate examples.

We consider estimation of the density of a multivariate response, that is not observed directly but only through measurements contaminated by additive error. Our focus is on the realistic sampling case of bivariate panel data (repeated contaminated bivariate measurements on each sample unit) with an unknown error distribution. Several factors can affect the performance of kernel deconvolution density estimators, including the choice of the kernel and the estimation approach of the unknown error distribution. As the choice of the kernel function is critically important, the class of flat-top kernels can have advantages over more commonly implemented alternatives. We describe different approaches for density estimation with multivariate panel responses, and investigate their performance through simulation. We examine competing kernel functions and describe a flat-top kernel that has not been used in deconvolution problems. Moreover, we study several nonparametric options for estimating the unknown error distribution. Finally, we also provide guidelines to the numerical implementation of kernel deconvolution in higher sampling dimensions.

Rural intersections account for around 30% of crashes in rural areas and 6% of all fatal crashes, representing a significant but poorly understood safety problem. Crashes at rural intersections are also problematic since high speeds on intersection approaches are present which can exacerbate the impact of a crash. Additionally, rural areas are often underserved with EMS services which can further contribute to negative crash outcomes. This paper describes an analysis of driver stopping behavior at rural T-intersections using the SHRP 2 Naturalistic Driving Study data. Type of stop was used as a safety surrogate measure using full/rolling stops compared to non-stops. Time series traces were obtained for 157 drivers at 87 unique intersections resulting in 1277 samples at the stop controlled approach for T-intersections. Roadway (i.e. number of lanes, presence of skew, speed limit, presence of stop bar or other traffic control devices), driver (age, gender, speeding), and environmental characteristics (time of day, presence of rain) were reduced and included as independent variables. Results of a logistic regression model indicated drivers were less likely to stop during the nighttime. However presence of intersection lighting increased the likelihood of full/rolling stops. Presence of intersection skew was shown to negatively impact stopping behavior. Additionally drivers who were traveling over the posted speed limit upstream of the intersection approach were less likely to stop at the approach stop sign.

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