Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics

In this paper, we consider a flexible semiparametric approach for estimating multivariate probability mass functions. The corresponding estimator is governed by a parametric starter, for instance a multivariate Poisson distribution with nonnegative cross correlations which is basically estimated through an expectation–maximization algorithm, and a nonparametric part which is an unknown weight discrete function to be smoothed through multiple binomial kernels. Our central focus is upon the selection matrix of bandwidths by the local Bayesian method. We additionally discuss the diagnostic model to enact an appropriate choice between the parametric, semiparametric and nonparametric approaches. Retaining a pure nonparametric method implies losing parametric benefices in this modelling framework. Practical applications, including a tail probability estimation, on multivariate count datasets are analyzed under several scenarios of correlations and dispersions. This semiparametic approach demonstrates superior performances and better interpretations compared to parametric and nonparametric ones.