Nonparametric density estimation based on beta prime kernel

Abstract

In this work, we propose beta prime kernel estimator for estimation of a probability density functions defined with nonnegative support. For the proposed estimator, beta prime probability density function used as a kernel. It is free of boundary bias and nonnegative with a natural varying shape. We obtained the optimal rate of convergence for the mean squared error (MSE) and the mean integrated squared error (MISE). Also, we use adaptive Bayesian bandwidth selection method with Lindley approximation for heavy tailed distributions and compare its performance with the global least squares cross-validation bandwidth selection method. Simulation studies are performed to evaluate the average integrated squared error (ISE) of the proposed kernel estimator against some asymmetric competitors using Monte Carlo simulations. Moreover, real data sets are presented to illustrate the findings.

Keywords:

• Beta prime kernel
• boundary bias
• density estimation
• mean integrated square error
• Bayesian bandwidth selection

Mathematics Subject Classification (2010):

• 62G07
• 41A25

Acknowledgements

The authors wish to thank the associate editor and the anonymous reviewers for their helpful comments and suggestions. This work was supported by Scientific Research Projects Coordination Unit of Istanbul Technical University with project number 40198.