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Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data

Yasmina Ziane (), Nabil Zougab () and Smail Adjabi ()
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Yasmina Ziane: University of Bejaia
Nabil Zougab: University of Bejaia
Smail Adjabi: University of Bejaia

Computational Statistics, 2018, vol. 33, issue 1, 299-318

Abstract: Abstract In this paper, we study the performance of the Birnbaum–Saunders-power-exponential (BS-PE) kernel and Bayesian local bandwidth selection in the context of kernel density estimation for nonnegative heavy tailed data. Our approach considers the BS-PE kernel estimator and treats locally the bandwidth h as a parameter with prior distribution. The posterior density of h at each point x (point where the density is estimated) is derived in closed form, and the Bayesian bandwidth selector is obtained by using popular loss functions. The performance evaluation of this new procedure is carried out by a simulation study and real data in web-traffic. The proposed method is very quick and very competitive in comparison with the existing global methods, namely biased cross-validation and unbiased cross-validation.

Keywords: Biased cross validation; Bayesian bandwidth selector; Integrated squared error; Loss functions; Prior distribution; Unbiased cross validation (search for similar items in EconPapers)
Date: 2018
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