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

Zhongguo Zheng; Kai-Tai Fang

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 language	English
Pages (from-to)	679-692
Number of pages	14
Journal	Statistica Sinica
Volume	4
Issue number	2
Publication status	Published - Jul 1994
Externally published	Yes

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Concentration probability
Fisher's bound of estimator
asymptotic efficiency

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https://www.jstor.org/stable/24305540

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

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.",

keywords = "Concentration probability, Fisher's bound of estimator, asymptotic efficiency",

author = "Zhongguo Zheng and Kai-Tai Fang",

note = "Funding Information: Research of Z. Zheng was supported partially by Hong Kong Baptist College, the NSFC and the Doctoral Program Foundation of China. Research of K. T. Fang was supported by the Hong Kong UPGC Grant. The authors are grateful to the referees and editors for their useful comments which led to improvement of this paper. Publisher copyright: {\textcopyright} 1994 Institute of Statistical Science, Academia Sinica",

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AU - Zheng, Zhongguo

AU - Fang, Kai-Tai

N1 - Funding Information: Research of Z. Zheng was supported partially by Hong Kong Baptist College, the NSFC and the Doctoral Program Foundation of China. Research of K. T. Fang was supported by the Hong Kong UPGC Grant. The authors are grateful to the referees and editors for their useful comments which led to improvement of this paper. Publisher copyright: © 1994 Institute of Statistical Science, Academia Sinica

PY - 1994/7

Y1 - 1994/7

N2 - 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.

AB - 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.

KW - Concentration probability

KW - Fisher's bound of estimator

KW - asymptotic efficiency

M3 - Journal article

SN - 1017-0405

VL - 4

SP - 679

EP - 692

JO - Statistica Sinica

JF - Statistica Sinica

IS - 2

ER -

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

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