Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions
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 . Its rate of convergence in probability is N − , 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 − 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.
Volume (Year): 9 (1993)
Issue (Month): 01 (January)
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