Ake: An R Package for Discrete and Continuous Associated Kernel Estimations

Wansouwé, Wanbitching E.; Somé, Sobom M.; Kokonendji, Célestin C.

doi:10.32614/rj-2016-045

Cited by 13 publications

(9 citation statements)

References 44 publications

(75 reference statements)

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“…where f (k) is the kth derivative or finite difference of the pdmf f under the existence of the centered moment of order k ≥ 2 of Z x,h . Concerning bandwidth matrix selections in a multivariate associated kernel estimator (8), one generally use the cross-validation technique (e.g., [10,20,28,33,34]). However, it is tedious and less precise.…”

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

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

confidence: 99%

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Kokonendji

Somé

2021

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“…Concerning bandwidth matrix selections in a multivariate associated kernel estimator (3.1), one generally use the cross-validation technique (e.g., [26,27,28,29,56]). However, it is tedious and less precise.…”

Section: Multivariate Orthant 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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“…The lognormal PDF was used explicitly for the construction of log-KDEs in [4], and more generally, for conducting asymmetric KDE on the support (0, ∞), in [9]. Other works that have considered the log-normal PDF for conducting asymmetric KDE include [6], [8], [7], and [22]. In the R environment, asymmetric KDE with lognormal PDF as kernels has been implemented through the dke.fun function from the package Ake [22].…”

Section: Kernelmentioning

confidence: 99%

“…Other works that have considered the log-normal PDF for conducting asymmetric KDE include [6], [8], [7], and [22]. In the R environment, asymmetric KDE with lognormal PDF as kernels has been implemented through the dke.fun function from the package Ake [22].…”

Section: Kernelmentioning

confidence: 99%

Positive data kernel density estimation via the logKDE package for R

Jones¹,

Nguyen²,

McLachlan³

2018

Preprint

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Kernel density estimators (KDEs) are ubiquitous tools for nonparametric estimation of probability density functions (PDFs), when data are obtained from unknown data generating processes. The KDEs that are typically available in software packages are defined, and designed, to estimate real-valued data. When applied to positive data, these typical KDEs do not yield bona fide PDFs. A log-transformation methodology can be applied to produce a nonparametric estimator that is appropriate and yields proper PDFs over positive supports. We call the KDEs obtained via this transformation log-KDEs. We derive expressions for the pointwise biases, variances, and mean-squared errors of the log-KDEs that are obtained via various kernel functions. Mean integrated squared error (MISE) and asymptotic MISE results are also provided and a plug-in rule for log-KDE bandwidths is derived. We demonstrate the log-KDEs methodology via our R package, logKDE. Real data case studies are provided to demonstrate the log-KDE approach.

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Ake: An R Package for Discrete and Continuous Associated Kernel Estimations

Cited by 13 publications

References 44 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

Positive data kernel density estimation via the logKDE package for R

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