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

Sobom M. Somé (), Célestin C. Kokonendji (), Smail Adjabi (), Naushad A. Mamode Khan () and Said Beddek ()
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Sobom M. Somé: Université Thomas SANKARA
Célestin C. Kokonendji: Université Bourgogne Franche-Comté
Smail Adjabi: University of Bejaia
Naushad A. Mamode Khan: University of Mauritius
Said Beddek: Université de Bouira

Computational Statistics, 2024, vol. 39, issue 2, No 21, 905-937

Abstract: Abstract The modified (or second version) gamma kernel of Chen [Probability density function estimation using gamma kernels, Annals of the Institute of Statistical Mathematics 52 (2000), pp. 471–480] should not be automatically preferred to the standard (or first version) 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 $$[0,\infty )^d$$ [ 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.

Keywords: Asymmetric kernel; Multivariate boundary kernel; Nonnegative data; Prior distribution; Semiparametric estimator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01327-7

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