A SMOOTHED MAXIMUM SCORE ESTIMATOR FOR THE BINARY RESPONSE MODEL
A SMOOTHED MAXIMUM SCORE ESTIMATOR FOR THE BINARY RESPONSE MODEL
复制标题
DOI：
10.2307/2951582
复制
发表时间：
1992-05-01
期刊：
影响因子：
6.1
通讯作者：
HOROWITZ, JL
中科院分区：
文献类型：
--
作者：
HOROWITZ, JL
Manski（1985）证明了在弱分布假设下二元响应模型的系数向量的最大分数估计量是一致的。Cavanagh（1987）和Kim and Pollard（1989）已经证明，n /3倍的中心最大分数估计量在分布上收敛于使某个高斯过程最大化的随机变量。极限分布的性质在很大程度上是未知的，Cavanagh、Kim和Pollard的结果不能用于应用中的推理。本文描述了一个改进的最大分数估计量，它是通过最大化平滑版的Manski分数函数得到的。在比Manski强一些但仍然很弱的分布假设下，中心平滑估计量是渐近正态的，收敛速率至少为N-2/5，并且可以任意接近N-1/2，这取决于某些平滑假设的强度。在所做的假设下，估计器的收敛速度是最快的。从数据中可以一致地估计出极限分布的参数，从而可以在样本足够大的情况下基于平滑估计器进行统计推断。
Manski (1985) has shown that the maximum score estimator of the coefficient vector of a binary response model is consistent under weak distributional assumptions. Cavanagh (1987) and Kim and Pollard (1989) have shown that N1/3 times the centered maximum score estimator converges in distribution to the random variable that maximizes a certain Gaussian process. The properties of the limiting distribution are largely unknown, and the result of Cavanagh and Kim and Pollard cannot be used for inference in applications. This paper describes a modified maximum score estimator that is obtained by maximizing a smoothed version of Manski's score function. Under distributional assumptions that are somewhat stronger than Manski's but still very weak, the centered smoothed estimator is asymptotically normal with a convergence rate that is at least N-2/5 and can be made arbitrarily close to N-1/2, depending on the strength of certain smoothness assumptions. The estimator's rate of convergence is the fastest possible under the assumptions that are made. The parameters of the limiting distribution can be estimated consistently from data, thereby making statistical inference based on the smoothed estimator possible with samples that are sufficiently large.