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September, 1983 Second Order Efficiency of Minimum Contrast Estimators in a Curved Exponential Family
Shinto Eguchi
Ann. Statist. 11(3): 793-803 (September, 1983). DOI: 10.1214/aos/1176346246

Abstract

This paper presents a sufficient condition for second order efficiency of an estimator. The condition is easily checked in the case of minimum contrast estimators. The $\alpha^\ast$-minimum contrast estimator is defined and proved to be second order efficient for every $\alpha, 0 < \alpha < 1$. The Fisher scoring method is also considered in the light of second order efficiency. It is shown that a contrast function is associated with the second order tensor and the affine connection. This fact leads us to prove the above assertions in the differential geometric framework due to Amari.

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Shinto Eguchi. "Second Order Efficiency of Minimum Contrast Estimators in a Curved Exponential Family." Ann. Statist. 11 (3) 793 - 803, September, 1983. https://doi.org/10.1214/aos/1176346246

Information

Published: September, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0519.62027
MathSciNet: MR707930
Digital Object Identifier: 10.1214/aos/1176346246

Subjects:
Primary: 62F10
Secondary: 62F12

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 3 • September, 1983
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