二元选择分位回归的自适应LASSO改进

为避免模型出现过拟合,将自适应LASSO变量选择方法引入二元选择分位回归模型,利用贝叶斯方法构建Gibbs抽样算法并在抽样中设置不影响预测结果的约束条件‖β‖=1以提高抽样值的稳定性.通过数值模拟,表明改进的模型有更为良好的参数估计效率、变量选择功能和分类能力.     

面板数据下带固定效应的线性回归模型的稳健变量选择

本文结合复合分位数回归和自适应LASSO惩罚方法为固定效应面板数据模型提供了一种稳健变量选择过程。先通过正向正交偏差变换消除固定效应,再利用自适应LASSO构造惩罚复合分位数回归目标函数,进而同时进行回归系数的估计和变量选择。在一些正则条件下,证明了所提出的估计具有Orcale性质。该方法不仅消除了固定效应对估计的影响,而且具有稳健性。模拟研究了所提出方法的有限样本性质并将其应用于实际数据分析。     

中国居民消费的特征分析——中基于两阶段面板分位回归

本文结合实际问题,提出一种两阶段面板数据分位回归方法,并使用该方法分析我国居民的消费特征。通过横向和纵向比较揭示三种不同收入人群的边际消费倾向的变化趋势。文章认为中等收入者的边际消费倾向趋于稳定,低收入者和高收入者的边际消费倾向都有上升的趋势。中国居民的边际消费倾向呈现"U"型,所以提高低收入者的消费不仅在于提高他们的收入,更重要的是缩小当前的贫富差距。     

基于LASSO复合分位数回归的钢材力学性能预测

钢材力学性能的提高对于提高钢材品质,充分适应市场需求有重要的意义.研究了热轧带钢的抗拉强度与各生产参数和工艺参数之间的关系,采用基于LASSO的复合分位数回归模型(Composite Quantile Regression,CQR),根据BIC准则选择合适的调整参数,选择出15个有重要影响的变量,建立基于这15个变量的预测模型.结果表明,将数据按70%和30%分成训练集和测试集,得到训练集的百分比误差(MAPE)和均方根误差(RMSE)分别为2.61%和23.42,测试集的百分比误差(MAPE)和均方根误差(RMSE)分别为2.58%和22.52.将本文所用的模型与两种不同的变量选择方法和三种不同的预测模型进行了对比,可得本文中所用的模型计算精度高,模型泛化能力强,为钢产品的设计和优化提供参考.     

删失混合效应模型的分位回归及变量选择

纵向数据常常用正态混合效应模型进行分析.然而,违背正态性的假定往往会导致无效的推断.与传统的均值回归相比较,分位回归可以给出响应变量条件分布的完整刻画,对于非正态误差分布也可以给稳健的估计结果.本文主要考虑右删失响应下纵向混合效应模型的分位回归估计和变量选择问题.首先,逆删失概率加权方法被用来得到模型的参数估计.其次,结合逆删失概率加权和LASSO惩罚变量选择方法考虑了模型的变量选择问题.蒙特卡洛模拟显示所提方法要比直接删除删失数据的估计方法更具优势.最后,分析了一组艾滋病数据集来展示所提方法的实际应用效果.     

面板数据分位数回归模型的参数估计与变量选择

本文研究了基于面板数据的分位数回归模型的变量选择问题.通过增加改进的自适应Lasso惩罚项,同时实现了固定效应面板数据的分位数回归和变量选择,得到了模型中参数的选择相合性和渐近正态性.随机模拟验证了该方法的有效性.推广了文献[14]的结论.     

面板数据分位数回归模型求解的模式搜索法

本文应用最优化理论,对固定效应的面板数据分位数回归模型,提出一种模式搜索方法,此方法可以同时估计出所有分位点处的解释变量系数和所有个体的固定效应值。进一步利用蒙特卡洛模拟比较现有文献中涉及的面板数据分位数回归方法,结果显示无论误差项是否满足经典假设,模式搜索分位数回归法较之其他分位数回归估计方法更为有效.     

缺失数据下超高维可加分位回归的变量筛选和选择

针对存在缺失数据的超高维可加分位回归模型,本文提出一种有效的变量筛选方法.具体而言,将典型相关分析的思想引入到最优变换的最大相关系数,通过协变量和模型残差最优变换后的最大相关系数重要变量的边际贡献进行排序,从而进行变量筛选.然后,在筛选的基础上,利用稀疏光滑惩罚进一步做变量选择.所提变量筛选方法有三点优势:(1)基于最优变换的最大相关可以更全面的反映响应变量对协变量的非线性依赖结构;(2)在迭代过程中利用残差可以获取模型的相关信息,从而提高变量筛选的准确度;(3)变量筛选过程和模型估计分开,可以避免对冗余协变量的回归.在适当的条件下,证明了变量筛选方法的确定性独立筛选性质以及稀疏光滑惩罚下估计量的稀疏性和相合性.同时,通过蒙特卡罗模拟给出了所提方法的表现并通过一组小鼠基因数据说明了所提方法的有效性.     

半参数空间分位回归模型的估计与变量选择

对于高维空间数据,利用半参数空间自回归进行建模,模型中会同时存在内生性、非线性、变量过多等问题。本文研究半参数空间分位回归模型,提出了新的估计程序:首先利用样条基函数,对模型中未知平滑函数进行逼近,解决非线性问题;然后运用特征向量空间滤波,将空间滞后因子转化为空间代理变量的线性组合,有效解决了内生性问题;利用再中心化影响函数,进行无条件分位回归建模,能够刻画不同分位水平下变量之间的关系;最后引入自适应Lasso惩罚,对高维线性部分进行变量选择,得到系数的稀疏估计,有效增强了模型的可解释性。数值模拟中对参数作不同的设置,展现了本文提出方法的有效性。最后,利用半参数空间分位回归模型分析了住房销售价格数据集。     

基于面板分位回归方法的我国金融发展对城乡收入差距影响分析

在收入差距的不同分位点上,金融发展对其的影响会展现出不一样的特征。由于我国区域金融发展不均,这一作用机制还具有显著的地区差异。本文利用面板分位回归模型和面板数据聚类方法探寻金融发展对贫富分化作用的分位点特征和地区差异。实证表明,我国大部分地区的金融发展加剧城乡收入差距的扩大,并且这一作用机制存在动态变化特征。当城乡收入差距从高分位点变动到低分位点时,金融发展拉大城乡收入差距的作用逐渐减缓,部分省份甚至具有金融发展抑制城乡收入差距扩大的效应。本文的研究结论将为业内人士和政府的相关决策提供参考依据。     

Adaptive Local Linear Quantile Regression

In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our ...     

失混合效应模型的分位回归及变量选择

纵向数据常常用正态混合效应模型进行分析.然而,违背正态性的假定往往会导致无效的推断.与传统的均值回归相比较,分位回归可以给出响应变量条件分布的完整刻画,对于非正态误差分布也可以给稳健的估计结果．本文主要考虑右删失响应下纵向混合效应模型的分位回归估计和变量选择问题．首先,逆删失概率加权方法被用来得到模型的参数估计．其次,结合逆删失概率加权和LASSO惩罚变量选择方法考虑了模型的变量选择问题.蒙特卡洛模拟显示所提方法要比直接删除删失数据的估计方法更具优势．最后,分析了一组艾滋病数据集来展示所提方法的实际应用效果．     

Fast Nonparametric Quantile Regression With Arbitrary Smoothing Methods

The calculation of nonparametric quantile regression curve estimates is often computationally intensive, as typically an expensive nonlinear optimization problem is involved. This article proposes a fast and easy-to-implement method for computing such estimates. The main idea is to approximate the costly nonlinear optimization by a sequence of well-studied penalized least squares-type nonparametric mean regression estimation problems. The new method can be paired with different nonparametric smoothing methods and can also be applied to higher dimensional settings. Therefore, it provides a unified framework for computing different types of nonparametric quantile regression estimates, and it also greatly broadens the scope of the applicability of quantile regression methodology. This wide applicability and the practical performance of the proposed method are illustrated with smoothing spline and wavelet curve estimators, for both uni- and bivariate settings. Results from numerical experiments suggest that estimates obtained from the proposed method are superior to many competitors. This article has supplementary material online.     

高维模型选择方法综述

模型选择是统计学的热点研究问题。近年来随着数据维数越来越高,传统模型选择方法的应用受到了很多制约。本文着重介绍高维模型选择的新方法,并讨论实现模型选择过程的一个重要环节,即调整参数的选取。最后文章总结归纳了未来可能的研究方向。     

���ع�ģ�͵�Smooth LASSO��Spline LASSO����ѡ��

??Considering a parameter estimation and variable selection problem in logistic regression, we propose Smooth LASSO and Spline LASSO. When the variables is continuous, using Smooth LASSO can select local constant coefficient in each group. However, in some case, the coefficient might be different and change smoothly. Using Spline Lasso to estimate parameter is more appropriate. In this article, we prove the reliability of the model by theory. Finally using coordinate descent algorithm to solve the model. Simulations show that the model works very effectively both in feature selection and prediction accuracy.     

Variable Selection for Logistic Regression via Smooth LASSO and Spline LASSO

Considering a parameter estimation and variable selection problem in logistic regression, we propose Smooth LASSO and Spline LASSO. When the variables is continuous, using Smooth LASSO can select local constant coefficient in each group. However, in some case, the coefficient might be different and change smoothly. Using Spline Lasso to estimate parameter is more appropriate. In this article, we prove the reliability of the model by theory. Finally using coordinate descent algorithm to solve the model. Simulations show that the model works very effectively both in feature selection and prediction accuracy.     

An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression

We propose and study a new iterative coordinate descent algorithm (QICD) for solving nonconvex penalized quantile regression in high dimension. By permitting different subsets of covariates to be relevant for modeling the response variable at different quantiles, nonconvex penalized quantile regression provides a flexible approach for modeling high-dimensional data with heterogeneity. Although its theory has been investigated recently, its computation remains highly challenging when p is large due to the nonsmoothness of the quantile loss function and the nonconvexity of the penalty function. Existing coordinate descent algorithms for penalized least-squares regression cannot be directly applied. We establish the convergence property of the proposed algorithm under some regularity conditions for a general class of nonconvex penalty functions including popular choices such as SCAD (smoothly clipped absolute deviation) and MCP (minimax concave penalty). Our Monte Carlo study confirms that QICD substantially improves the computational speed in the p ? n setting. We illustrate the application by analyzing a microarray dataset.