The adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data Adaptive gamma-BSPE kernel density estimation for nonnegative heavy-tailed data
Article Sidebar
Main Article Content
Abstract
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.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences the right to be the first publication of the document, licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License that allows others to share the work with an acknowledgement of authorship and publication in the journal.
- Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.
References
D. K. Bhaumik, K. Kapur and R. D. Gibbons, Testing parameters of a gamma distribution for small samples, Technometrics, 51(3) (2009), 326–334.
S. X. Chen, Probability Density Function Estimation Using Gamma Kernels, Ann. Inst. Statist. Math., 52(3) (2000), 471–480.
X. Jin and J. Kawczak, Birnbaum-Saunders and lognormal kernel estimators for modelling durations in high frequency financial data, Annals of Economics and Finance, 4 (2003), 103–124.
C. Marchant, K. Bertin, V. Leiva and H. Saulo, Generalized Birnbauma Saunders kernel density estimators and an analysis of financial data, Comput. Statist. Data Anal., 63 (2013), 1–15.
L. Markovich, Gamma-weibull kernel estimation of the heavy-tailed densities, arXiv preprint arXiv: 1604.06522. (2016), 1–10.
O. Scaillet, Density estimation using inverse and reciprocal inverse Gaussian kernels, J. Nonparametr. Stat., 16(1-2) (2004), 217–226.
Y. Ziane, S. Adjabi and N. Zougab, Adaptive Bayesian bandwidth selection in asymmetric kernel density estimation for nonnegative heavy-tailed data, J. Appl. Stat., 42(8) (2015), 1645–1658.
Y. Ziane, N. Zougab and S. Adjabi, Birnbauma Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy-tailed data, Comput. Statist., 33(1) (2018), 299–318.
Y. Ziane, N. Zougab and S. Adjabi, Body tail adaptive kernel density estimation for nonnegative heavy-tailed data, Monte Carlo Methods Appl., 27(1), (2021), 57–69.