Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation

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

doi:10.1016/j.csda.2014.02.002

Cited by 51 publications

(44 citation statements)

References 30 publications

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“…Furthermore, the cross-validation method has the inconvenience that it is not always consistent depending on the discrete kernel and data used. Finally, it would be interesting to investigate Bayesian estimation of bandwidth by using other discrete kernels and adaptive approach (Zougab et al 2014b).…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…However, in this paper and following Senga Kiessé et al (2015) and, Zougab et al (2014) we choose α = 0.5 and β = √ n. The choice of β which depends on the sample size n is important for the consistency of nonparametric kernel estimator of pmf and permits the convergence of Bayesian bandwidths estimators to zero (h j → 0 while n → ∞ for j = 1, . .…”

Section: Q(h (T)mentioning

confidence: 98%

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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“…Four bivariate density functions F 1 , F 2 , F 3 , and F 4 [21][22][23][24] are provided to analyze the performance of the above four calculating methods.…”

Section: Comparisons Of the Calculating Methods Of Bandwidthmentioning

confidence: 99%

Non-parametric load extrapolation based on load extension for semi-axle of wheel loader

Wang

Jiang

2017

Advances in Mechanical Engineering

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Load extrapolation is the paramount step in compiling load spectra of the mechanical components. To avoid the limitation of the stationary processes in parametric extrapolation methods, the non-parametric extrapolation method is widely investigated in recent years. However, the accuracy of kernel density estimation of the large load cycles in existing non-parametric methods should be still improved. Aiming at this issue, a non-parametric rain-flow extrapolation method based on load extension is presented. In this method, combining with non-parametric extrapolation model and Markov chain Monte Carlo method, the measured load-time histories for semi-axle in different operating sections are extended and extrapolated. The extrapolated load spectra curves and the relative damage ratio are compared with the results obtained by the existing rain-flow extrapolation methods. The results show that the proposed method can realize the reasonable extrapolation of load-time histories.

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Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation

Cited by 51 publications

References 30 publications

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

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

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

Non-parametric load extrapolation based on load extension for semi-axle of wheel loader

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