Bayesian local bandwidth selector in multivariate associated kernel estimator for joint probability mass functions

Belaid, Nawal; Adjabi, Smaïl; Kokonendji, Célestin C.; Zougab, Nabil

doi:10.1080/00949655.2016.1181178

Cited by 11 publications

(8 citation statements)

References 24 publications

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“…However, it is tedious and less precise. Many papers have recently proposed Bayesian approaches (e.g., [6,7,13,14,35,36] and references therein). In particular, they have recommended local Bayesian for discrete smoothing of pmf (e.g., [6,7,37]) and adaptive one for continuous smoothing of pdf (e.g., [13,35,36]).…”

Section: Proposition 2 Under the Assumption (A1) On F Then The Estimator F N In (8) Of F Verifiesmentioning

confidence: 99%

“…Here, B(x, h) tends to x/(x + 1) ∈ [0, 1) when h → 0 and the new Definition 1 holds. This first-order and under-dispersed binomial kernel is introduced in [28] which becomes very useful for smoothing count distribution through small or moderate sample size; see, e.g., [6,7,37] for Bayesian approaches and some references therein. In addition, we have the standard Poisson kernel where K Poisson x,h follows the equi-dispersed Poisson distribution with…”

Section: Example 3 (Standard Count) Let T +mentioning

confidence: 99%

“…The nonparametric topic of associated kernels, which is adaptable to any support T + d of probability density or mass function (pdmf), is widely studied in very recent years. We can refer to [6][7][8][9][10][11][12][13][14][15] for general results and more specific developments on associated kernel orthant distributions using classical cross-validation and Bayesian methods to select bandwidth matrices. Thus, a natural question of flexible semiparametric modeling now arises for all these multivariate orthant datasets.…”

Section: Introductionmentioning

confidence: 99%

“…Empirical univariate (in diagonal), bivariate (off diagonal) and trivariate (at the corner) variation(6) and dispersion (3) indexes.…”

mentioning

confidence: 99%

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Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji

Somé

2021

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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.

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Section: Proposition 2 Under the Assumption (A1) On F Then The Estimator F N In (8) Of F Verifiesmentioning

confidence: 99%

Section: Example 3 (Standard Count) Let T +mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Empirical univariate (in diagonal), bivariate (off diagonal) and trivariate (at the corner) variation(6) and dispersion (3) indexes.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji

Somé

2021

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“…The nonparametric topic of associated kernels, which is adaptable to any support T + d of probability density or mass function (pdmf), is widely studied in very recent years. We can refer to [7,8,12,13,29,43,51,52,61,62] for general results and more specific developments on associated kernel orthant distributions using classical cross-validation and Bayesian methods to select bandwidth matrices. Thus, a natural question of a flexible semiparametric modelling now arises for all these multivariate orthant datasets.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji,

Somé

2021

Preprint

Self Cite

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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.

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Bayesian Selection of Adaptive Bandwidth in Non-homogeneous Poisson Process Kernel Estimators for the Intensity Function

Badiane

Ngom

Manga

2022

Trends in Mathematics

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Bayesian local bandwidth selector in multivariate associated kernel estimator for joint probability mass functions

Cited by 11 publications

References 24 publications

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Bayesian Selection of Adaptive Bandwidth in Non-homogeneous Poisson Process Kernel Estimators for the Intensity Function

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