ABSTRACT
This chapter details the computational algorithms which are markedly different and less statistically intuitive than their concise descriptions, but which lead to important gains in computational efficiency, in terms of execution time and memory management. It outlines the R package and associated R scripts which implement the algorithms. The chapter elaborates binned estimation as a method of computing kernel estimators based on Fast Fourier Transform methods. It explores recursive algorithms for the exact computation of the derivatives and functionals of the multivariate normal density. The chapter considers numerical optimisation for matrix-valued inputs. Binned estimators can vastly improve the computational efficiency of kernel estimators for large sample sizes via fast Fourier transform (FFT) operations. To maintain this computational gain, an efficient method is required for computing higher order derivatives of the normal density as they are one of the inputs for the FFTs.
