## The Annals of Statistics

### The $n^{-2}$-Order Mean Squared Errors of the Maximum Likelihood and the Minimum Logit Chi-Square Estimator

Takeshi Amemiya

#### Abstract

The $n^{-2}$ order mean squared errors of the maximum likelihood and the minimum chi-square estimator of the logit regression model are derived and the latter is shown to be superior for many parameter values considered. The maximum likelihood is shown to be better if the bias of each estimator is corrected to the order of $n^{-1}$; however, the difference is shown to be negligibly small in many practical situations.

#### Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 488-505.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345004

Digital Object Identifier
doi:10.1214/aos/1176345004

Mathematical Reviews number (MathSciNet)
MR568716

Zentralblatt MATH identifier
0436.62032

JSTOR
Amemiya, Takeshi. The $n^{-2}$-Order Mean Squared Errors of the Maximum Likelihood and the Minimum Logit Chi-Square Estimator. Ann. Statist. 8 (1980), no. 3, 488--505. doi:10.1214/aos/1176345004. https://projecteuclid.org/euclid.aos/1176345004
• See Correction: Takeshi Amemiya. Corrections: The $N^{-2}$-Order Mean Squared Errors of the Maximum Likelihood and the Minimum Logit Chi-Squared Estimator. Ann. Statist., Vol. 12, Iss. 2 (1984), 783.