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

Ziane, Yasmina; Zougab, Nabil; Adjabi, Smaïl

doi:10.1007/s00180-017-0712-8

Cited by 12 publications

(4 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…measured in Kilo Octet from the world cup (French, June 1998) server. These data are collected for n = 312 queries [8].…”

Section: Application To Real Ht Datamentioning

confidence: 99%

See 1 more Smart Citation

adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data

Ziane¹,

Zougab²,

Adjabi³

2022

J. Innov. Appl. Math. Comput. Sci

Self Cite

View full text Add to dashboard Cite

In this work, we consider the nonparametric estimation of the probability density function for nonnegative heavy-tailed (HT) data. The objective is first to propose a new estimator that will combine two regions of observations (high and low density). While associating a gamma kernel to the high-density region and a BS-PE kernel to the low-density region. Then, to compare the proposed estimator with the classical estimator in order to evaluate its performance. The choice of bandwidth is investigated by adopting the popular cross-validation technique and two variants of the Bayesian approach. Finally, the performances of the proposed and the classical estimators are illustrated by a simulation study and real data.

show abstract

“…measured in Kilo Octet from the world cup (French, June 1998) server. These data are collected for n = 312 queries [8].…”

Section: Application To Real Ht Datamentioning

confidence: 99%

“…In this work, we are interested in estimating the heavy-tailed data density with nonnegative support [7] and [8]. This data type requires special methods because of its specific characteristics: slow decay to zero and rare observations in the tail.…”

Section: Introductionmentioning

confidence: 99%

adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data

Ziane¹,

Zougab²,

Adjabi³

2022

J. Innov. Appl. Math. Comput. Sci

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several different models relating to univariate and multivariate BS distributions can be found in the works of Athayde et al, Balakrishnan and Saulo, Barros et al, Bhatti, Cancho et al, Cordeiro et al, Cordeiro and Lemonte, Desmond et al, Díaz‐García and Domínguez‐Molina, Díaz‐García and Leiva, Ferreira et al, Fierro et al, Fonseca and Cribari‐Neto, Genç, Gomes et al, Guiraud et al, Gupta and Akman, Hashimoto et al, Jamalizadeh and Kundu, Khosravi et al, Kundu, Leiva et al, Lemonte and Cordeiro, Lemonte and Ferrari, Martínez‐Flórez et al, Marchant et al, Olmos et al, Onar and Padgett, Ortega et al, Owen, Owen and Padgett, Park and Padgett, Patriota, Pescim et al, Pourmousa et al, Raaijmakers, Romeiro et al, Reina et al, Reyes et al, Sanhueza et al, Vilca and Leiva‐Sánchez, Volodin and Dzhungurova, and Ziane et al Recently, some survival analytic methods have been developed based on BS and related models. For example, one may refer to the works of Leão, Leão et al, and Balakrishnan and Liu .…”

Section: Concluding Remarks and Further Readingmentioning

confidence: 99%

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

110

View full text Add to dashboard Cite

Birnbaum and Saunders introduced a two-parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix-variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research. KEYWORDSBayes estimators, EM algorithm, Fisher information matrix, hazard function, length-biased distribution, moments and inverse moments, probability density function, stochastic orderings, TP 2 property 4

show abstract

“…In nonparametric and semiparametric setups, one can see for example [40], [9], [35], [36], [4] and [42] for Bayesian adaptive approach using univariate Birnbaum-Saunders kernel, scaled inverse Chi-Squared, (univariate and multiple) standard gamma kernel, multiple binomial and multivariate Gaussian kernel, respectively. See also, [6], [3] and [41] with Bayesian local approaches.…”

Section: Introductionmentioning

confidence: 99%

Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths

Somé¹,

Kokonendji²,

Adjabi³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a product of univariate standard and modified ones, are here introduced for nonparametric and semiparametric smoothing of unknown orthant densities with support [0, ∞) d . Asymptotical properties of these multivariate associated kernel estimators are established. Bayesian estimation of adaptive bandwidth vectors using multiple pure combined gamma smoothers, and in semiparametric setup, are exactly derived under the usual quadratic function. The simulation results and four illustrations on real datasets reveal very interesting advantages of the proposed combined approach for nonparametric smoothing, compare to both pure standard and pure modified gamma kernel versions, and under integrated squared error and average log-likelihood criteria.

show abstract

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

Cited by 12 publications

References 31 publications

adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data

adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Multiple combined gamma kernel estimations for nonnegative data with Bayesian adaptive bandwidths

Contact Info

Product

Resources

About