Evaluation of numerical integration methods for kernel averaged predictors

Abstract

In spatial applications, kernel averaged predictors have been used in disciplines such as entomology and ecology. Most of the approaches entomologists and ecologists use are ad- hoc implementations of kernel averaged predictors. In this report, I discuss a general way to compute the kernel averaged predictors. I evaluate two numerical integration methods to approximate kernel averaged predictors. Using a simulation study, I evaluate the approximation of kernel averaged predictors with a combination of three factors. The combinations consist of Gaussian and uniform kernel functions, quadrature rule and Monte Carlo numerical integration, and various numbers of numerical integration points. I illustrate the approximation of the kernel averaged predictor using field data on Hessian fly abundance. The results of the approximations are evaluated by comparing the reliability of the estimated regression coefficients and the run time under each setting. My simulation experiment and data illustration show that the rate of convergence using quadrature rule is faster than using Monte Carlo integration. In addition, my results demonstrate that a small number of numerical integration points can achieve a reasonable approximation for the kernel averaged predictors, which result in reliable statistical inference.