Local Asymptotic Normality of Families of Distributions

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


In a number of interesting papers of Hájek, LeCam, and other authors, it was proved that many important properties of statistical estimators follow from the asymptotic normality of the logarithm of the likelihood ratio for neighborhood hypotheses (for values of parameters close to each other) regardless of the relation between the observations which produced the given likelihood function. This chapter is devoted to an investigation of the conditions under which this property is valid for various models and to corollaries of this property.


Likelihood Ratio Loss Function Asymptotic Normality Fisher Information Matrix Asymptotic Efficiency 
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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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