A Modelling Approach for Bandwidth Selection in Kernel Density Estimation

Brewer, Mark

doi:10.1007/978-3-662-01131-7_22

Cited by 12 publications

(9 citation statements)

References 8 publications

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“…From now we study the Bayesian global approach to estimate the bandwidth diagonal matrix H = Diag d (h j ) j in (6). Following some authors as Brewer (1998), Zhang et al (2006) and Zougab et al (2013a), we treat the bandwidth matrix H as a random variable with a given prior distribution π (H). The Bayesian inference concerning H conditional on data is made via the posterior density π (H|data) given by π (H|X 1 , X In our study, we assume that each component h j of H = Diag d (h j ) j has a prior distribution denoted π (h j ); e.g., beta and gamma distributions.…”

Section: Bayesian Global Bandwidth Selectormentioning

confidence: 99%

“…This approach has received an attention in the literature, particularly in the univariate context for symmetric kernels. We can see, Brewer (1998Brewer ( , 2000 who proposed the global and adaptive Bayesian approach. Gangopadhyay and Cheung (2002), Kulasekera and Padgett (2006) and Kuruwita, Kulasekera, and Padgett (2010) proposed a Bayesian local bandwidth selection.…”

Section: Introductionmentioning

confidence: 97%

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Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions

Belaid

Adjabi

Zougab

et al. 2016

Journal of the Korean Statistical Society

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a b s t r a c tThis paper proposed a nonparametric estimator for probability mass function of multivariate data. The estimator is based on discrete multivariate associated kernel without correlation structure. For the choice of the bandwidth diagonal matrix, we presented the Bayes global method against the likelihood cross-validation one, and we used the Bayesian Markov chain Monte Carlo (MCMC) method for deriving the global optimal bandwidth. We have compared the proposed method with the cross-validation method. The performance of both methods is evaluated under the integrated square error criterion through simulation studies based on for univariate and multivariate models. We also presented applications of the proposed methods to bivariate and trivariate real data. The obtained results show that the Bayes global method performs better than cross-validation one, even for the Poisson kernel which is the very bad discrete associated kernel among binomial, discrete triangular and Dirac discrete uniform kernels.

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Section: Bayesian Global Bandwidth Selectormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions

Belaid

Adjabi

Zougab

et al. 2016

Journal of the Korean Statistical Society

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“…The adaptive asymmetric kernel estimator of f is given bŷ where K x,h i is the asymmetric associated kernel and h i is the variable bandwidth associated with each observation x i . The main objective is to derive the variable bandwidths h i for Equation (2) by treating h i as a random quantity with a prior distribution π(·).…”

Section: Adaptive Bayesian Bandwidth Selectionmentioning

confidence: 99%

“…The posterior distribution and the Bayes estimators for each variable bandwidth can be derived exactly using the Bayes theorem and both quadratic and entropy loss functions. The Baysian approach with global, local and adaptive versions to bandwidth selection has received considerable attention, see [2,3,8] for univariate symmetric kernel density estimation, [12,13] for univariate kernel density estimation with censored data, [22,23] for discrete associated kernel estimators and [6,7,9,21,24] for multivariate kernel density estimation. These previous studies show that this approach is a very good alternative to classical methods.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data

Ziane

Adjabi

Zougab

2015

Journal of Applied Statistics

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In this paper, we consider an interesting problem on adaptive Birnbaum-Saunders-power-exponential (BS-PE) kernel density estimation for nonnegative heavy-tailed (HT) data. Treating the variable bandwidths h i , i = 1, . . . , n of adaptive BS-PE kernel as parameters, we then propose a conjugate prior and estimate the h i 's by using the popular quadratic and entropy loss functions. Explicit formulas are obtained for the posterior and Bayes estimators. Comparison simulations with global unbiased cross-validation bandwidth selection technique were conducted under four HT distributions. Finally, two applications based on HT real data are presented and analyzed.

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“…In order to avoid numerical underflow in practice, we modified the acceptance probability ρ as follows (see Brewer 1998): |y 1 , y 2 , . .…”

Section: An Mcmc Algorithmmentioning

confidence: 99%

Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

2015

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This work takes advantage of semiparametric modelling which improves significantly in many situations the estimation accuracy of the purely nonparametric approach. Herein for semiparametric estimations of probability mass function (pmf) of count data, and an unknown count regression function (crf), the kernel used is a binomial one and the bandiwdth selection is investigated by developing Bayesian approaches. About the latter, Bayes local and global bandwidth approaches are used to establish data-driven selection procedures in semiparametric framework. From conjugate beta prior distributions of the smoothing parameter and under the squared errors loss function, Bayes estimate for pmf is obtained in closed form. This is not available for the crf which is computed by the Markov Chain Monte Carlo technique. Simulation studies demonstrate that both proposed methods perform better than the classical cross-validation procedures, in particular the smoothing quality and execution times are optimized. All applications are made on real data sets. B Nabil Zougab

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A Modelling Approach for Bandwidth Selection in Kernel Density Estimation

Cited by 12 publications

References 8 publications

Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions

Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions

Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data

Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

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