## The Annals of Statistics

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

Shinto Eguchi

#### 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.

#### Article information

Source
Ann. Statist., Volume 11, Number 3 (1983), 793-803.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346246

Digital Object Identifier
doi:10.1214/aos/1176346246

Mathematical Reviews number (MathSciNet)
MR707930

Zentralblatt MATH identifier
0519.62027

JSTOR