Parameter estimation by minimizing a probability generating function-based power divergence

Abstract

Generating function-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generating function. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases.

Keywords:

• Density power divergence
• Hellinger distance
• Jeffreys’ divergence
• M-estimation
• Probability generating function

Subject classification code:

• 62F10
• 62F12

Acknowledgments

The authors would like to thank the referees for their helpful comments that greatly improve this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Ministry of Higher Education, Malaysia under the FRGS grants FP014-2012A and FP045-2015A.