A new Bayesian wavelet thresholding estimator of nonparametric regression

ABSTRACT

The methods of estimation of nonparametric regression function are quite common in statistical application. In this paper, the new Bayesian wavelet thresholding estimation is considered. The new mixture prior distributions for the estimation of nonparametric regression function by applying wavelet transformation are investigated. The reversible jump algorithm to obtain the appropriate prior distributions and value of thresholding is used. The performance of the proposed estimator is assessed with simulated data from well-known test functions by comparing the convergence rate of the proposed estimator with respect to another by evaluating the average mean square error and standard deviations. Finally by applying the developed method, density function of galaxy data is estimated.

KEYWORDS:

• Nonparametric regression
• wavelet transformation
• thresholding
• conjugate prior distribution
• reversible jump algorithm

Acknowledgments

The authors would like to thank the referees and editors for supplying extremely helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.