Multivariate generalized Birnbaum—Saunders kernel density estimators

ABSTRACT

In this article, we first propose the classical multivariate generalized Birnbaum–Saunders kernel estimator for probability density function estimation in the context of multivariate non negative data. Then, we apply two multiplicative bias correction (MBC) techniques for multivariate kernel density estimator. Some properties (bias, variance, and mean integrated squared error) of the corresponding estimators are also investigated. Finally, the performances of the classical and MBC estimators based on family of generalized Birnbaum–Saunders kernels are illustrated by a simulation study.

KEYWORDS:

• Integrated squared error
• Multiplicative bias correction
• Multivariate non negative data

Acknowledgments

The authors thank the editor, an associate editor, and anonymous referees for their valuable comments that allowed us to improve this article.