The Annals of Statistics

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

Shinto Eguchi

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Affine connection ancillary subspace of estimator curvature curved exponential family Fisher consistency Fisher information Fisher scoring method information loss maximum likelihood estimator minimum contrast estimator $\Gamma$-transversality searching curve of estimator second order efficiency

Citation

Eguchi, Shinto. Second Order Efficiency of Minimum Contrast Estimators in a Curved Exponential Family. Ann. Statist. 11 (1983), no. 3, 793--803. doi:10.1214/aos/1176346246. https://projecteuclid.org/euclid.aos/1176346246


Export citation