众数自适应Lasso回归的统计推断
Statistical Inference of Mode Regression with Adaptive Lasso
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摘要: 本文给出了自适应Lasso的众数回归模型,用来对众数回归模型的变量进行选择.对比传统的均值回归模型和中位数回归模型,众数回归在解决重尾、多峰分布问题时更加稳健.众数回归模型的主要估计方法是核估计方法, 当自变量的数目较大时,该方法会产生难以忽略的计算误差.本文在核估计方法的众数回归模型基础上添加惩罚项,并通过自适应Lasso方法进行参数估计, 有效的剔除了贡献率低的自变量,同时提高了计算的准确性. 本文详细阐述了该计算方法, 并在一些正则条件下,给出了模型的参数的估计方法和估计值的渐近正态性.模拟实验和实证分析研究了所提方法在有限样本下的性质.对比均值回归模型和传统的众数回归模型,添加自适应Lasso惩罚项的众数回归模型极大地提高了参数估计的准确性.Abstract: In this paper, an adaptive Lasso mode regression model is proposed to solve the problem of variable selection in mode regression model. Compared with the traditional mean regression and median regression, mode regression is robust when the distribution is heavy-tail or asymmetric. Kernel estimation is widely used in mode regression. When coping with high dimension, the method will result in calculation errors that hard to ignore. In this paper, the adaptive Lasso penalty is added to estimated parameters based on the mode regression model of the kernel estimation method, and the independent variables with low contribution rate are effectively eliminated. Therefore, the method can improve the accuracy of the calculation. The calculation method is described in detail in this paper, and this paper proposes the estimation methods of the parameters of the model and the asymptotic normality of the estimated values under some regular conditions. The simulation experiment and empirical analysis are performed to investigate the properties of the proposed method in finite sample. Compared with the traditional mode regression model and the mean regression model, the mode regression model with adaptive Lasso penalty greatly improves the accuracy of parameter estimation.