On Fisher's Bound for Stable Estimators with Extension to the Case of Hilbert Parameter Space

Zhongguo Zheng, Kai-Tai Fang

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Abstract

Fisher's bound for asymptotic variances has been shown to hold almost everywhere for several classes of estimators in LeCam (1953), Bahadur (1964) and Wong (1992). Wong's result applies to estimators with arbitrary asymptotic distributions, provided a certain continuity condition is satisfied. In this paper we improve on Wong's result by removing the continuity condition. We also generalize the result to the case where the parameter space is separable Hilbert.
Original languageEnglish
Pages (from-to)679-692
Number of pages14
JournalStatistica Sinica
Volume4
Issue number2
Publication statusPublished - Jul 1994
Externally publishedYes

User-Defined Keywords

  • Concentration probability
  • Fisher's bound of estimator
  • asymptotic efficiency

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