Properties of Estimators in the Regular Case

  • I. A. Ibragimov
  • R. Z. Has’minskii
Part of the Applications of Mathematics book series (SMAP, volume 16)


In the preceding chapter, some general properties of estimators in the case when the family of distributions obeys the LAN property were established. In particular, a minimax lower bound on the quality of various estimates for a large class of loss functions were derived. The main purpose of the present chapter is to prove the asymptotic efficiency of a maximum likelihood estimator and of a large class of Bayesian and generalized Bayesian estimators for regular families of experiments. Evidently, certain new restrictions on the families under consideration will be required.


Loss Function Gaussian White Noise Maximum Likelihood Estimator Consistent Estimator Bayesian Estimator 
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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • I. A. Ibragimov
    • 1
  • R. Z. Has’minskii
    • 2
  1. 1.LOMILeningradUSSR
  2. 2.Doz., Institut Problem Peredači Inf.MoscowUSSR

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