A new non parametric estimator for Pdf based on inverse gamma distribution

Mousa, Arwa; Hassan, Marwa K. H.; Fathi, Aria

doi:10.1080/03610926.2014.972575

Cited by 12 publications

(2 citation statements)

References 21 publications

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“…Now, we point out eight main and useful families of univariate semicontinuous associated kernels for (9) and satisfying (K1) and (K2). Which are gamma (G) of [43] (see also [44]), inverse gamma (Ig) (see also [45]) and log-normal 2 (LN2) by [41], inverse Gaussian (IG) and reciprocal inverse Gaussian by [46] (see also [47]), log-normal 1 (LN1) and Birnbaum-Saunders by [48] (see also [49,50]), and Weibull (W) of [51] (see also [50]). It is noteworthy that the link between LN2 of [41] and LN1 of [48] is through changing (x, h) to (x exp(h 2 ), 2 log(1 + h).…”

Section: Semicontinuous Associated Kernelsmentioning

confidence: 99%

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: Semicontinuous Associated Kernelsmentioning

confidence: 99%

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji

Somé

2021

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“…Now, we point out eight main and useful families of univariate semicontinuous associated kernels for (3.2) and satisfying (K1) and (K2). Which are gamma (G) of [9] (see also [14]), inverse gamma (Ig) (see also [42]) and log-normal 2 (LN2) by [37], inverse Gaussian (IG) and reciprocal inverse Gaussian by [46] (see also [18]), log-normal 1 (LN1) and Birnbaum-Saunders by [19] (see also [38,41]), and Weibull (W) of [45] (see also [41]). It is noteworthy that the link between LN2 of [37] and LN1 of [19] is through changing (x, h) to (x exp(h 2 ), 2 log(1 + h).…”

Section: Semicontinuous Associated Kernelsmentioning

confidence: 99%

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji,

Somé

2021

Preprint

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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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Asymmetric Kernels: An Introduction

Hirukawa

2018

Asymmetric Kernel Smoothing

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A new non parametric estimator for Pdf based on inverse gamma distribution

Cited by 12 publications

References 21 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

Asymmetric Kernels: An Introduction

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