Bayesian selector of adaptive bandwidth for gamma kernel density estimator on [0,∞): simulations and applications

Abstract

Bayesian bandwidth selections in continuous associated kernel estimation of probability density function are very good alternatives to classical methods like cross-validation techniques. In this paper, we examined the behavior of Bayesian variable bandwidths in gamma kernel estimation, developed theoretically in Wansouwé et al. [Ake: An R Package for Discrete and Continuous Associated Kernel Estimations, The R journal 8 (2016), pp. 259–276], and appropriated to smooth densities of support $[0,\infty ).$ Simulations studies point out remarkable performance of the proposed approach, comparing to the global cross-validation bandwidth selection, and under integrated squared errors. Two applications related to CO₂ emissions and medical bills of bodily injury claims, respectively, are finally made.

Keyword:

• Asymmetric kernel
• Nonnegative data
• Prior distribution
• Unbiased cross-validation

AMS SUBJECT CLASSIFICATION:

• 62G07
• 62G99

Acknowledgements

The author sincerely thank an Associate Editor and two anonymous referees for their valuable comments. We are also grateful to Khoirin Nisa for her attentive reading.