Two new nonparametric kernel distribution estimators based on a transformation of the data

ABSTRACT

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set.

Keywords:

• Distribution estimation
• stochastic approximation algorithm
• smoothing
• curve fitt ing
• Bias reduction

2010 Mathematics Subject Classifications:

• Primary 62E20
• 62L20
• Secondary 65D10

Acknowledgments

The author would like to thank the Editor and two anonymous referees for their thoughtful comments and remarks, which helped us to focus on improving the original version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.