Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models
Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models
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DOI：
10.1017/s0266466600009361
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发表时间：
1995-06
影响因子：
0.8
通讯作者：
Lung-fei Lee
中科院分区：
文献类型：
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作者：
Lung-fei Lee
在本文中，我们研究了 Lerman 和 Manski（C. Manski 和 D. McFadden (eds.)，《离散数据结构分析与计量经济学应用》第 305-319 页，剑桥：麻省理工学院出版社，1981 年）引入的用于估计离散选择模型的模拟最大似然估计量的渐近展开偏差。这种偏差的发生是由于对数似然函数导数的非线性以及跨观测值的选择概率的统计独立模拟误差。当每个观察的模拟随机变量的数量至少不与样本大小一样快地增加时，这种偏差可能是模拟最大似然估计的渐近展开中的主要偏差。如果模拟随机变量的数量仅以样本大小的平方根的速度增加，则正确归一化的模拟最大似然估计甚至在其极限分布中具有渐近偏差。引入偏差调整可以减少偏差。一些蒙特卡罗实验已经证明了偏差调整程序的有用性。
In this article, we investigate a bias in an asymptotic expansion of the simulated maximum likelihood estimator introduced by Lerman and Manski (pp. 305–319 in C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications, Cambridge: MIT Press, 1981) for the estimation of discrete choice models. This bias occurs due to the nonlinearity of the derivatives of the log likelihood function and the statistically independent simulation errors of the choice probabilities across observations. This bias can be the dominating bias in an asymptotic expansion of the simulated maximum likelihood estimator when the number of simulated random variables per observation does not increase at least as fast as the sample size. The properly normalized simulated maximum likelihood estimator even has an asymptotic bias in its limiting distribution if the number of simulated random variables increases only as fast as the square root of the sample size. A bias-adjustment is introduced that can reduce the bias. Some Monte Carlo experiments have demonstrated the usefulness of the bias-adjustment procedure.