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

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Author Info
Horowitz, Joel L.
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 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 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.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 9 (1993)
Issue (Month): 01 (January)
Pages: 1-18
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:9:y:1993:i:01:p:1-18_00

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  1. Emmanuel Guerre & Hyungsik Roger Moon, 2005. "A Study of a Semiparametric Binary Choice Model with Integrated Covariates," IEPR Working Papers 05.37, Institute of Economic Policy Research (IEPR). [Downloadable!]
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  2. Walter Beckert & Daniel McFadden, 2007. "Maximal uniform convergence rates in parametric estimation problems," CeMMAP working papers CWP28/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
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This page was last updated on 2009-11-24.

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