Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

TL;DR

This paper develops Bayesian bandwidth selection methods for semiparametric modeling of multivariate nonnegative data, introducing a flexible estimator combining parametric and nonparametric parts, with diagnostics for model choice.

Contribution

It proposes a novel Bayesian bandwidth selection approach for multivariate nonnegative data, integrating parametric and nonparametric modeling with diagnostic tools.

Findings

Effective Bayesian bandwidth methods for semicontinuous data

Flexible semiparametric estimators outperform purely parametric models

Diagnostic tools assist in choosing appropriate modeling approaches

Abstract

Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi- and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.