面板数据的贝叶斯Elastic Net分位数回归方法及其应用研究

本文首次将Elastic Net这种用于高度相关变量的惩罚方法用于面板数据的贝叶斯分位数回归,并基于非对称Laplace先验分布推导所有参数的后验分布,进而构建Gibbs抽样。为了验证模型的有效性,本文将面板数据的贝叶斯Elastic Net分位数回归方法(BQR. EN)与面板数据的贝叶斯分位数回归方法(BQR)、面板数据的贝叶斯Lasso分位数回归方法(BLQR)、面板数据的贝叶斯自适应Lasso分位数回归方法(BALQR)进行了多种情形下的全方位比较,结果表明BQR. EN方法适用于具有高度相关性、数据维度很高和尖峰厚尾分布特征的数据。进一步地,本文就BQR. EN方法在不同扰动项假设、不同样本量的情形展开模拟比较,验证了新方法的稳健性和小样本特性。最后,本文选取互联网金融类上市公司经济增加值(EVA)作为实证研究对象,检验新方法在实际问题中的参数估计与变量选择能力,实证结果符合预期。     

样本选择参数分位回归模型及其在工资分布分解中的应用

在工资差距分解问题中,研究者经常会遇到样本选择偏差问题,直接忽略会导致最终估计结果产生严重偏差,同时在众多工资差距分解方法中,相比于均值分解,分布分解方法更受研究者青睐。针对参数分位回归,本文首次提出可加形式与非可加形式的样本选择参数分位回归（SSPQR）模型,并基于这两类样本选择参数分位回归模型给出修正样本选择偏差后的参数分位回归工资差距分布分解方法。运用上述方法及已有的工资分布分解方法,借助CHNS2015年度城镇数据,本文研究了我国城镇男女工资差距及差距分解问题,得出以下结论：①男女工资差距主要来源是性别歧视问题;②经过样本选择偏差修正后,实际的工资差距更大,歧视问题更严重;③男女工资差距程度在不同分位点上结果不同,换句话说,我们不能简单地仅从平均水平来判断工资差距程度;④与其他已有方法计算结果比较发现,SSPQR计算的工资差距程度更大。     

Oracle Inequalities for Convex Loss Functions with Nonlinear Targets

This article considers penalized empirical loss minimization of convex loss functions with unknown target functions. Using the elastic net penalty, of which the Least Absolute Shrinkage and Selection Operator (Lasso) is a special case, we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear, this inequality also provides an upper bound of the estimation error of the estimated parameter vector. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically of the same order as that of the oracle. If the target is linear, we give sufficient conditions for consistency of the estimated parameter vector. We briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions covered by our framework.     

Understanding Estimators of Treatment Effects in Regression Discontinuity Designs

In this paper, we propose two new estimators of treatment effects in regression discontinuity designs. These estimators can aid understanding of the existing estimators such as the local polynomial estimator and the partially linear estimator. The first estimator is the partially polynomial estimator which extends the partially linear estimator by further incorporating derivative differences of the conditional mean of the outcome on the two sides of the discontinuity point. This estimator is related to the local polynomial estimator by a relocalization effect. Unlike the partially linear estimator, this estimator can achieve the optimal rate of convergence even under broader regularity conditions. The second estimator is an instrumental variable estimator in the fuzzy design. This estimator will reduce to the local polynomial estimator if higher order endogeneities are neglected. We study the asymptotic properties of these two estimators and conduct simulation studies to confirm the theoretical analysis.     

Inferences for a Partially Varying Coefficient Model With Endogenous Regressors

In this article, we propose a new class of semiparametric instrumental variable models with partially varying coefficients, in which the structural function has a partially linear form and the impact of endogenous structural variables can vary over different levels of some exogenous variables. We propose a three-step estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic normality of these proposed estimators are established. Moreover, a generalized F-test is developed to test whether the functional coefficients are of particular parametric forms with some underlying economic intuitions, and furthermore, the limiting distribution of the proposed generalized F-test statistic under the null hypothesis is established. Finally, we illustrate the finite sample performance of our approach with simulations and two real data examples in economics.     

并购企业支付方式选择与内部控制、资本结构——基于logistic回归模型的实证研究

以2008—2010年间沪市上市公司的922起并购案例为研究样本,通过logistic回归方法,实证分析了内部控制水平、资本结构对并购支付方式选择产生的影响。研究发现：与现金支付相比,资产负债率越低,股权支付的可能性越大;内部控制水平越低,股权支付的可能性越小。内部控制水平与资本结构对资产支付及其他支付方式（以混合支付为主）影响不显著。     

On pseudo-values for regression analysis in competing risks models

For regression on state and transition probabilities in multi-state models Andersen et al. (Biometrika 90:15–27, 2003) propose a technique based on jackknife pseudo-values. In this article we analyze the pseudo-values suggested for competing risks models and prove some conjectures regarding their asymptotics (Klein and Andersen, Biometrics 61:223–229, 2005). The key is a second order von Mises expansion of the Aalen-Johansen estimator which yields an appropriate representation of the pseudo-values. The method is illustrated with data from a clinical study on total joint replacement. In the application we consider for comparison the estimates obtained with the Fine and Gray approach (J Am Stat Assoc 94:496–509, 1999) and also time-dependent solutions of pseudo-value regression equations.     

Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Huber's estimator has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.     

Robust nonparametric estimation with missing data

In this paper, under a nonparametric regression model, we introduce two families of robust procedures to estimate the regression function when missing data occur in the response. The first proposal is based on a local M$M$-functional applied to the conditional distribution function estimate adapted to the presence of missing data. The second proposal imputes the missing responses using the local M$M$-smoother based on the observed sample and then estimates the regression function with the completed sample. We show that the robust procedures considered are consistent and asymptotically normally distributed. A robust procedure to select the smoothing parameter is also discussed.