Bayesian adaptive bandwidth selector for multivariate discrete kernel estimator

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

doi:10.1080/03610926.2017.1346807

Cited by 12 publications

(12 citation statements)

References 18 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%

“…It was introduced in the multivariate setup by Aitchison and Aitken [38] and investigated as a discrete associated kernel which is symmetric to the target x by [28] in univariate case; see [7] for a Bayesian approach in multivariate setup. Note here that its normalized constant is always 1 = C n .…”

Section: Example 1 (Categorical)mentioning

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%

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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 1 (Categorical)mentioning

confidence: 99%

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

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji

Somé

2021

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“…For multi-dimensional data, besides bandwidth matrix, the product kernel is usually used to solve high-dimensional problems. Belaid et al (2018) [21] applied the adaptive bandwidth selected by the Bayesian method to the high-dimensional discrete kernel. Gramacki and Gramacki (2017) [22] used the FFT method to solve some problems of the bandwidth matrix.…”

Section: Introductionmentioning

confidence: 99%

Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships

Zhang

et al. 2021

Mathematics

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The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix.

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Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths

et al. 2023

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Bayesian adaptive bandwidth selector for multivariate discrete kernel estimator

Cited by 12 publications

References 18 publications

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships

Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths

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