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首页> 外文期刊>Transportation Research Part B: Methodological >A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance-covariance matrix
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A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance-covariance matrix

机译：用全方差-协方差矩阵估计随机系数模型的维数诅咒的蒙特卡洛实验

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摘要

When the dimension of the vector of estimated parameters increases, simulation based methods become impractical, because the number of draws required for estimation grows exponentially with the number of parameters. In simulation methods, the lack of empirical identification when the number of parameters increases is usually known as the "curse of dimensionality" in the simulation methods. We investigate this problem in the case of the random coefficients Logit model. We compare the traditional Maximum Simulated Likelihood (MSL) method with two alternative estimation methods: the Expectation-Max imization (EM) and the Laplace Approximation (HH) methods that do not require simula tion. We use Monte Carlo experimentation to investigate systematically the performance of the methods under different circumstances, including different numbers of variables, sam ple sizes and structures of the variance-covariance matrix. Results show that indeed MSL suffers from lack of empirical identification as the dimensionality grows while EM deals much better with this estimation problem. On the other hand, the HH method, although not being simulation-based, showed poor performance with large dimensions, principally because of the necessity of inverting large matrices. The results also show that when MSL is empirically identified this method seems superior to EM and HH in terms of ability to recover the true parameters and estimation time.
机译：当估计参数的向量的维数增加时，基于仿真的方法变得不切实际，因为估计所需的绘制次数随参数的数量呈指数增长。在模拟方法中，当参数数量增加时缺乏经验识别，通常被称为模拟方法中的“维数诅咒”。我们在随机系数Logit模型的情况下调查此问题。我们将传统的最大模拟似然（MSL）方法与两种替代估计方法进行了比较：不需要模拟的最大期望最大化（EM）方法和拉普拉斯逼近（HH）方法。我们使用蒙特卡洛实验系统地研究了在不同情况下方法的性能，包括不同数量的变量，样本大小和方差-协方差矩阵的结构。结果表明，随着维数的增长，MSL确实缺乏经验鉴定，而EM在处理此估计问题上要好得多。另一方面，HH方法虽然不是基于仿真的，但在大尺寸情况下却表现出较差的性能，这主要是因为需要对大矩阵求逆。结果还表明，当凭经验确定MSL时，该方法在恢复真实参数和估计时间方面似乎优于EM和HH。

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