Flexible Semiparametric Kernel Estimation with Bayesian Local Bandwidths and Diagnostics for Multivariate Count Data

While parametric models have fulfilled a prominent role in terms of modelling multivariate data, nonparametric kernel smoothings [1] are recently envisaged for count data. Multivariate count data appear in a wide range of fields like environments (e.g., different kinds of plantation), marketing (e.g., purchases of different products) or epidemiology (e.g., different types of a disease). In this paper, we elaborate two flexible semiparametric approaches governed by the multivariate Poisson with nonnegative cross correlations (from the common covariance µ 0 such that µ 0 =0 or µ 0 >0) for estimating multivariate probability mass functions. In the jungle of multivariate count distributions, we used the so-called generalized dispersion index [2] to compare several distributions between them. Our semiparametric method is then developed through expectation-maximisation scheme [3] and maximum likelihood method to estimate the parameters of the correlated and uncorrelated parametric Poisson departures. Also, the multiple binomial kernel with local Bayesian bandwidths [4] is used for the nonparametric part. Practical diagnostic criteria like the empirical integrated squared errors ISE 0 and the logarithm of the weight functions [5] are here opted to select the correct approach according to the data analysis. For the latter