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Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions

Published online by Cambridge University Press:  11 February 2009

Joel L. Horowitz
Joel L. Horowitz
Affiliation:
University of Iowa
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Abstract

The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and, after centering and suitable normalization, asymptotically normally distributed under weak assumptions [5]. Its rate of convergence in probability is N−h/(2h+1), where h ≥ 2 is an integer whose value depends on the strength of certain smoothness assumptions. This rate of convergence is faster than that of the maximum score estimator of Manski [11,12], which converges at the rate N−1/3 under assumptions that are somewhat weaker than those of the smoothed estimator. In this paper I prove that under the assumptions of smoothed maximum score estimation, N−h/(2h+1) is the fastest achievable rate of convergence of an estimator of the coefficient vector of a binary response model. Thus, the smoothed maximum score estimator has the fastest possible rate of convergence. The rate of convergence is defined in a minimax sense so as to exclude superefficient estimators.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 1 , January 1993 , pp. 1 - 18
Copyright
Copyright © Cambridge University Press 1993

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