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On a fundamental optimality of the maximum likelihood estimator

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  • Cheng, Ping
  • Fu, James C.

Abstract

It is well-known that the rate of exponential convergence for any consistent estimator is less than or equal to the Bahadur bound. In this paper we have proven, for the one-dimensional case, that the rate of exponential convergence for the maximum likelihood estimator (m.l.e.) attains the Bahadur bound if and only if the underlying distribution is a member of the exponential family of distributions.

Suggested Citation

  • Cheng, Ping & Fu, James C., 1986. "On a fundamental optimality of the maximum likelihood estimator," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 173-178, June.
    • Handle: RePEc:eee:stapro:v:4:y:1986:i:4:p:173-178
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    Cited by:

    1. J. Fu & Gang Li & D. Zhao, 1993. "On large deviation expansion of distribution of maximum likelihood estimator and its application in large sample estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 477-498, September.

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