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Adaptive gamma-BSPE kernel density estimatimation for nonnegative heavy tailed data
Yasmina Ziane  1, *@  , Nabil Zougab  2@  , Smail Adjabi  1@  
1 : Research unit LaMOS, Faculty of Exact Sciences, Bejaia University, 06000 Bejaia, Algeria  -  Website
2 : Research unit LaMOS, Faculty of technology, Bejaia University, 06000 Bejaia, Algeria;  -  Website
* : Corresponding author

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 to the high density region a gamma kernel and to the low density region a BS-PE kernel. Then, to compare the proposed estimator with the classical estimator in order to evaluate the performance of the new estimator. The choice of bandwidth is investigated by adopting the popular cross-validation technique and two variants of bayesian approach. Finally, the performances of the proposed estimator and the classical estimator are illustrated by a simulation study and real data.



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