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Article

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

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Laboratoire de Mathématiques de Besançon UMR 6623 CNRS-UBFC, Université Bourgogne Franche-Comté, 16 Route de Gray, 25030 Besançon CEDEX, France
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Laboratoire d’Analyse Numérique Informatique et de BIOmathématique, Université Joseph KI-ZERBO, Ouagadougou 03 BP 7021, Burkina Faso
*
Author to whom correspondence should be addressed.
Current address: Laboratoire Sciences et Techniques, Université Thomas SANKARA, Ouagadougou 12 BP 417, Burkina Faso.
Academic Editor: Eddy Kwessi
Received: 28 January 2021 / Revised: 19 February 2021 / Accepted: 1 March 2021 / Published: 4 March 2021
(This article belongs to the Special Issue Directions in Statistical Modelling)
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. View Full-Text
Keywords: associated kernel; Bayesian selector; dispersion index; model diagnostics; multivariate distribution; variation index; weighted distribution associated kernel; Bayesian selector; dispersion index; model diagnostics; multivariate distribution; variation index; weighted distribution
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MDPI and ACS Style

Kokonendji, C.C.; Somé, S.M. Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics. Stats 2021, 4, 162-183. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010013

AMA Style

Kokonendji CC, Somé SM. Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics. Stats. 2021; 4(1):162-183. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010013

Chicago/Turabian Style

Kokonendji, Célestin C., and Sobom M. Somé 2021. "Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics" Stats 4, no. 1: 162-183. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010013

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