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# Second Order Efficiency of Minimum Contrast Estimators in a Curved Exponential Family

Shinto Eguchi
The Annals of Statistics
Vol. 11, No. 3 (Sep., 1983), pp. 793-803
Stable URL: http://www.jstor.org/stable/2240642
Page Count: 11
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## 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 α*-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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