Ake: An R Package for Discrete and Continuous Associated Kernel Estimations

Kernel estimation is an important technique in exploratory data analysis. Its utility relies on its ease of interpretation, especially based on graphical means. The Ake package is introduced for univariate density or probability mass function estimation and also for continuous and discrete regression functions using associated kernel estimators. These associated kernels have been proposed due to their specific features of variables of interest. The package focuses on associated kernel methods appropriate for continuous (bounded, positive) or discrete (count, categorical) data often found in applied settings. Furthermore, optimal bandwidths are selected by cross-validation for any associated kernel and by Bayesian methods for the binomial kernel. Other Bayesian methods for selecting bandwidths with other associated kernels will complete this package in its future versions; particularly, a Bayesian adaptive method for gamma kernel estimation of density functions is developed. Some practical and theoretical aspects of the normalizing constant in both density and probability mass functions estimations are given.