Nearly unbiased estimation in a biparametric exponential family

Abstract

We consider two analytical and a bootstrap bias correction scheme existing in the literature for maximum likelihood estimators (MLEs) in the special case of a particular biparametric exponential family, the estimators being obtained from i.i.d. samples. We assess the performances of the estimators through numerical simulations for three particular cases of the family explored here. We observe that the two analytical proposals display very similar behavior for these distributions and that all proposed estimators are effective in reducing bias and mean square error of the MLEs.

Keywords:

• Bias corrections
• Biparametric exponential family
• Maximum likelihood

Acknowledgements

We gratefully acknowledge the financial support from the Brazilian governmental institution CNPq. We also would like to thank an anonymous referee for suggestions that led to an improved version of this work.