分位数变系数模型基于核光滑的变量选择

分位数变系数模型是一种稳健的非参数建模方法.使用变系数模型分析数据时,一个自然的问题是如何同时选择重要变量和从重要变量中识别常数效应变量.本文基于分位数方法研究具有稳健和有效性的估计和变量选择程序.利用局部光滑和自适应组变量选择方法,并对分位数损失函数施加双惩罚,我们获得了惩罚估计.通过BIC准则合适地选择调节参数,提出的变量选择方法具有oracle理论性质,并通过模拟研究和脂肪实例数据分析来说明新方法的有用性.数值结果表明,在不需要知道关于变量和误差分布的任何信息前提下,本文提出的方法能够识别不重要变量同时能区分出常数效应变量.     

The cumulative quantile regression function with censored and truncated covariate

In this paper, we consider the empirical estimator of the cumulative quantile regression (CQR) functionwhen the covariate is subjected to random truncation and censorship. Strong Gaussian approximations for the associated CQR process are established under appropriate assumptions. A functional law of the iterated logarithm for the CQR process is also derived. These results provide a foundation for the asymptotic theory of functional statistics based on these processes.     

Concave group methods for variable selection and estimation in high-dimensional varying coefficient models

The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. We study the problem of variable selection and estimation in this model in the sparse, high-dimensional case. We develop a concave group selection approach for this problem using basis function expansion and study its theoretical and empirical properties. We also apply the group Lasso for variable selection and estimation in this model and study its properties. Under appropriate conditions, we show that the group least absolute shrinkage and selection operator (Lasso) selects a model whose dimension is comparable to the underlying model, regardless of the large number of unimportant variables. In order to improve the selection results, we show that the group minimax concave penalty (MCP) has the oracle selection property in the sense that it correctly selects important variables with probability converging to one under suitable conditions. By comparison, the group Lasso does not have the oracle selection property. In the simulation parts, we apply the group Lasso and the group MCP. At the same time, the two approaches are evaluated using simulation and demonstrated on a data example.     

Some recent developments in modeling quantile treatment effects

This paper provides a selective review of the recent developments on econometric/statistical modeling in quantile treatment effects under both selection on observables and on unobservables.First,we discuss identification,estimation and inference of quantile treatment effects under the framework of selection on observables.Then,we consider the case where the treatment variable is endogenous or self-selected,for which an instrumental variable method provides a powerful tool to tackle this problem.Finally,some extensions are discussed to the data-rich environments,to the regression discontinuity design,and some other approaches to identify quantile treatment effects are also discussed.In particular,some future research works in this area are addressed.     

The adaptive lasso in high-dimensional sparse heteroscedastic models

In this paper we study the asymptotic properties of the adaptive Lasso estimate in high-dimensional sparse linear regression models with heteroscedastic errors. It is demonstrated that model selection properties and asymptotic normality of the selected parameters remain valid but with a suboptimal asymptotic variance. A weighted adaptive Lasso estimate is introduced and investigated. In particular, it is shown that the new estimate performs consistent model selection and that linear combinations of the estimates corresponding to the non-vanishing components are asymptotically normally distributed with a smaller variance than those obtained by the “classical” adaptive Lasso. The results are illustrated in a data example and by means of a small simulation study.     

Bridge estimators and the adaptive lasso under heteroscedasticity

In this paper we investigate penalized least squares methods in linear regression models with heteroscedastic error structure. It is demonstrated that the basic properties with respect to model selection and parameter estimation of bridge estimators, Lasso and adaptive Lasso do not change if the assumption of homoscedasticity is violated. However, these estimators do not have oracle properties in the sense of Fan and Li (2001) if the oracle is based on weighted least squares. In order to address this problem we introduce weighted penalized least squares methods and demonstrate their advantages by asymptotic theory and by means of a simulation study.     

Variable selection via quantile regression with the process of Ornstein-Uhlenbeck type

Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to be heteroscedastic,while in composite quantile regression,we require that the noise process be homoscedastic so that the slopes are invariant across quantiles.Similar to the independent noise case,the proposed quantile estimators are root-n consistent and asymptotic normal.Furthermore,the adaptive least absolute shrinkage and selection operator(LASSO)is applied for the purpose of variable selection.As a result,the quantile estimators are consistent in variable selection,and the nonzero coefficient estimators enjoy the same asymptotic distribution as their counterparts under the true model.Extensive numerical simulations are conducted to evaluate the performance of the proposed approaches and foreign exchange rate data are analyzed for the illustration purpose.     

无交叉多指标分位数回归模型中的估计与推断

在过去的30年中分位数回归模型的研究已十分深入.然而在实际的应用场景中,由传统估计方法所得到的分位数回归估计量,经常会在不同分位数水平上出现互相交叉的现象,这给分位数回归模型的实际应用造成了解释和预测上的困难.为解决这个问题,本文提出一种带单调约束的半参数多指标分位数回归模型的研究框架.首先将半参数多指标分位数回归模型与充分降维模型相结合,并利用两者间的联系获得指标估计量的相合估计.之后使用张量积样条方法拟合半参数模型在单调约束条件下的非参数结构.通过数值模拟的方式比较所提方法与现有可行方案所得结果在平均预测误差上的差异,实验结果和实际案例的结果都验证了本文所提出模型的可行性.     

Quantile regression based on counting process approach under semi-competing risks data

In this paper, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. The estimation of quantile regression parameters for the non-terminal event is complicated. We cannot make inference on the non-terminal event without extra assumptions. Thus, we handle this problem by assuming that the joint distribution of the terminal event and the non-terminal event follows a parametric copula model with unspecified marginal distributions. We use the stochastic property of the martingale method to estimate the quantile regression parameters under semi-competing risks data. We also prove the large sample properties of the proposed estimator, and introduce a model diagnostic approach to check model adequacy. From simulation results, it shows that the proposed estimator performs well. For illustration, we apply our proposed approach to analyze a real data.     

Composing the cumulative quantile regression function and the Goldie concentration curve

The model we discuss in this paper deals with inequality in distribution in the presence of a covariate. To elucidate that dependence, we propose to consider the composition of the cumulative quantile regression (CQR) function and the Goldie concentration curve, the standardized counterpart of which gives a fraction to fraction plot of the response and the covariate. It has the merit of enhancing the visibility of inequality in distribution when the latter is present. We shall examine the asymptotic properties of the corresponding empirical estimator. The associated empirical process involves a randomly stopped partial sum process of induced order statistics. Strong Gaussian approximations of the processes are constructed. The result forms the basis for the asymptotic theory of functional statistics based on these processes.     

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多元非参数分位数回归常常是难于估计的, 为了降低维数同时保持非参数估计的灵活性, 人们常常用单指标的方法模拟响应变量的条件分位数. 本文主要研究单指标分位数回归的变量选择. 以最小化平均损失估计为基础, 我们通过最小化具有SCAD惩罚项的平均损失进行变量选择和参数估计. 在正则条件下, 得到了单指标分位数回归SCAD变量选择的Oracle性质, 给出了SCAD变量选择的计算方法, 并通过模拟研究说明了本文所提方法变量选择的样本性质.     

Asymptotic properties of Lasso in high-dimensional partially linear models

We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size. We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model. Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions, we derive the oracle inequalities for the prediction risk and the estimation error. We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model. In addition, we derive the rate of convergence of the estimator of the nonparametric function. We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.     

Asymptotic properties of a particular nonlinear regression quantile estimation

In this paper we shall be concerned with the asymptotic properties of the regression quantile estimation in the nonlinear regression time series models. For these, first we prove the strong consistency and derive the asymptotic normality of the regression quantile estimators for a particular sinusoidal regression model with a simple harmonic component. Next, we extend the results to more complicated sinusoidal models of several harmonic components.     

Autoregressive process modeling via the Lasso procedure

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. We derive theoretical results establishing various types of consistency. In particular, we derive conditions under which the Lasso estimator for the autoregressive coefficients is model selection consistent, estimation consistent and prediction consistent. Simulation study results are reported.     

An effective method to reduce the computational complexity of composite quantile regression

In this article, we aim to reduce the computational complexity of the recently proposed composite quantile regression (CQR). We propose a new regression method called infinitely composite quantile regression (ICQR) to avoid the determination of the number of uniform quantile positions. Unlike the composite quantile regression, our proposed ICQR method allows combining continuous and infinite quantile positions. We show that the proposed ICQR criterion can be readily transformed into a linear programming problem. Furthermore, the computing time of the ICQR estimate is far less than that of the CQR, though it is slightly larger than that of the quantile regression. The oracle properties of the penalized ICQR are also provided. The simulations are conducted to compare different estimators. A real data analysis is used to illustrate the performance.     

Reduction principles for quantile and Bahadur–Kiefer processes of long-range dependent linear sequences

In this paper we consider quantile and Bahadur–Kiefer processes for long range dependent linear sequences. These processes, unlike in previous studies, are considered on the whole interval (0, 1). As it is well-known, quantile processes can have very erratic behavior on the tails. We overcome this problem by considering these processes with appropriate weight functions. In this way we conclude strong approximations that yield some remarkable phenomena that are not shared with i.i.d. sequences, including weak convergence of the Bahadur–Kiefer processes, a different pointwise behavior of the general and uniform Bahadur–Kiefer processes, and a somewhat “strange” behavior of the general quantile process.     

SIMEX Estimation for Composite Quantile Regression Model with Measurement Error

Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample properties of the proposed method are studied by a simulation study, and a real example is analyzed.     

宏观因素对房地产行业信用风险的影响研究——基于BALQR模型的实证

以2008年1月至2014年9月相关数据为基础,利用贝叶斯adaptive Lasso分位数回归(BALQR)模型对影响房地产业信用风险的宏观经济因素进行了分析.结果表明,在任何分位点上,对我国房地产行业信用风险影响最大的均是GDP增长率,其次是CPI增长率和消费者信心指数增长率,其中前者为负向作用后两者为正向作用,而资本市场的景气状态则对房地产行业信用风险基本没有显著作用.不过,在不同分位点上,不同宏观因素在房地产行业的不同信用风险水平上的影响程度又存在差异性.     

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??Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample properties of the proposed method are studied by a simulation study, and a real example is analyzed.     

一类混合序列下分位数估计的一致渐近正态性

本文在混合序列下, 研究了分位数估计的一致渐近正态性. 在一定条件下其收敛速度达到. 所得结果可以应用到风险度量VaR分位数估计.