## Abstract

In this paper, a behavior of the moment generating function based estimator for the natural parameter θ of a natural exponential family on R is studied. This estimator, say θ̂_{n,s}, depends on the sample size n and on an auxiliary variable s controlled by the experimenter, and is obtained as a solution of an equation generated by equating the theoretical moment generating function with its empirical counterpart. For fixed n, necessary and sufficient conditions for the existence and uniqueness of θ̂_{n,s} with probability 1 are presented. Asymptotically it is shown that for any fixed s,θ̂_{ n,s} is strongly consistent for θ as n→∞; and for any fixed n,θ̂_{ n,s} converges to the maximum likelihood estimator for θ as s→0. Moreover, under suitable normalization, the limiting distribution of θ̂_{n,s}, as either n→∞ and s→0, or as s→0 and n→∞, is shown to coincide with that of the maximum likelihood estimator. Such asymptotic results suggest, in some situations, the use of θ̂_{n,s} for large values of n and small values of s as an alternative to the ordinary maximum likelihood estimator.

Original language | English |
---|---|

Pages (from-to) | 279-291 |

Number of pages | 13 |

Journal | Journal of Statistical Planning and Inference |

Volume | 35 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1993 |

## Keywords

- Moment generating function based estimator
- asymptotic efficiency
- maximum likelihood estimator
- natural exponential family

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics