分位数回归技术综述

普通最小二乘回归建立了在自变量X=x下因变量Y的条件均值与X的关系的线性模型。而分位数回归（Quantile Regression）则利用自变量X和因变量y的条件分位数进行建模。与普通的均值回归相比,它能充分反映自变量X对于因变量y的分布的位置、刻度和形状的影响,有着十分广泛的应用,尤其是对于一些非常关注尾部特征的情况。文章介绍了分位数回归的概念以及分位数回归的估计、检验和拟合优度,回顾了分位数回归的发展过程以及其在一些经济研究领域中的应用,最后做了总结。     

中国农村居民收入差距的分位数回归解析

通过对1997～2009年中国农村居民收入差距进行分位数回归发现:工资性收入的增长是农村居民收入差距扩大的最主要原因,而财产性收入以及转移性收入则发挥着缩小农村居民收入差距的作用,家庭经营收入对收入差距的影响较小。出现这种结果的原因在于农民工流动的不稳定性导致农村居民家庭收入构成出现较大的波动,从而导致这一时期农村居民收入差距波动。     

分位数回归与上证综指VaR研究

把极端分位数所具有的行为特征应用到VaR的研究中,建立上海股市收益率的条件分位数回归模型,描述其在极端分位数下的变化趋势。同时选取适当的尾部模型,并在此基础之上应用外推法预测非常极端分位数下的条件VaR,并与直接由分位数回归模型预测的结果进行比较。结果表明：两种方法得到的结果变化趋势都是一致的,由外推法预测的结果相对小一些。     

阿基米德Copula分位数回归曲线推导与模拟

文章把分位数回归理论和相关结构函数Copula结合起来,介绍了分位数回归和相关结构函数Copula,给出了阿基米德Copula和Copula分位数回归曲线的定义,推导出了阿基米德Copu-la分位数回归曲线。最后,通过模拟研究表明Copula分位数回归估计方法的精确性。     

基于分位数回归的中国居民收入和消费的实证分析

阐述制约中国内需不足的几个主要因素,利用描述性统计和非参数方法重点考察中国居民收入差距的现状及其对扩大内需的重要影响.同时利用分位数回归技术对中国城镇和农村按收入等级划分的居民消费状况进行实证分析,结果表明:居民收入差距的确是制约中国内需不足的重要因素,不同收入阶层其边际消费倾向大不相同,并估算出这种消费倾向的具体值.从收入差距的视角提出了提高中国国内居民消费水平以便扩大内需的政策建议.     

分位数回归及应用简介

文章介绍了分位数回归法的概念、算法及主流统计软件R和SAS计算时的语法,并通过实例与以普通最小二乘法为基础的线性回归进行了对比,展现了分位数回归的巨大魅力。     

无条件分位数回归：文献综述与应用实例

条件分位数回归(conditional quantile regression,CQR)方法已成为经济学实证研究的常用方法之一。由于CQR结果的经济学阐释基于过多甚至是不必要的控制变量,这与人们所关心的问题有可能并不一致。例如,在劳动经济学对教育回报的研究中,无论个体的年龄,性别与家庭特征如何,教育程度对于个人收入的异质性影响是人们关注的重点,即人们想了解收入关于教育程度的无条件分位数估计。本文旨在介绍近年来发展起来的无条件分位数回归(unconditional quantile regression,UQR)技术并梳理相关文献。特别地,本文介绍三种重要的无条件分位数回归模型：Firpo, Fortin和Lemieux(2009)提出的的再中心化影响函数(recentered influence function, RIF) 回归,Frolich和Melly(2010)提出的无条件分位数处理效应模型与Powell(2010)提出的一般无条件分位数回归。另外,论文还运用一个研究居民收入分配格局变化对其医疗支出影响的实例详细说明了新方法的应用。     

基于分位数回归模型的证券市场风险研究

文章利用分位数回归模型对我国上证与深证市场进行实证研究表明,该模型能有效度量证券市场的在险价值,对证券市场的风险度量有助于投资者认识股市风险,将有助于投资者做出正确的投资决策。     

分位数回归的理论再说明及实例分析

文章从次序统计量的角度给出了分位数回归方法合理性的说明,给出R软件的实现过程并通过实例给出了分位数回归结果的解释。     

一种刻画不同水平研究对象的统计方法:分位数回归

一般线性回归分析的是研究对象的平均水平受到其它因素影响的程度大小,难以知道处在不同水平的研究对象受各种因素影响程度.文章介绍分数回归方法,以便能让更多的读者对这种新的统计研究方法有所了解.     

Non-parametric Quantile Regression with Censored Data

Abstract.  Censored regression models have received a great deal of attention in both the theoretical and applied statistics literature. Here, we consider a model in which the response variable is censored but not the covariates. We propose a new estimator of the conditional quantiles based on the local linear method, and give an algorithm for its numerical implementation. We study its asymptotic properties and evaluate its performance on simulated data sets.     

Quantile Regression via the EM Algorithm

The three-parameter asymmetric Laplace distribution (ALD) has received increasing attention in the field of quantile regression due to an important feature between its location and asymmetric parameters. On the basis of the representation of the ALD as a normal-variance–mean mixture with an exponential mixing distribution, this article develops EM and generalized EM algorithms, respectively, for computing regression quantiles of linear and nonlinear regression models. It is interesting to show that the proposed EM algorithm and the MM (Majorization–Minimization) algorithm for quantile regressions are really the same in terms of computation, since the updating formula of them are the same. This provides a good example that connects the EM and MM algorithms. Simulation studies show that the EM algorithm can successfully recover the true parameters in quantile regressions.     

Semiparametric Hierarchical Composite Quantile Regression

In biological, medical, and social sciences, multilevel structures are very common. Hierarchical models that take the dependencies among subjects within the same level are necessary. In this article, we introduce a semiparametric hierarchical composite quantile regression model for hierarchical data. This model (i) keeps the easy interpretability of the simple parametric model; (ii) retains some of the flexibility of the complex non parametric model; (iii) relaxes the assumptions that the noise variances and higher-order moments exist and are finite; and (iv) takes the dependencies among subjects within the same hierarchy into consideration. We establish the asymptotic properties of the proposed estimators. Our simulation results show that the proposed method is more efficient than the least-squares-based method for many non normally distributed errors. We illustrate our methodology with a real biometric data set.     

Local Linear Additive Quantile Regression

Abstract.  We consider non-parametric additive quantile regression estimation by kernel-weighted local linear fitting. The estimator is based on localizing the characterization of quantile regression as the minimizer of the appropriate 'check function'. A backfitting algorithm and a heuristic rule for selecting the smoothing parameter are explored. We also study the estimation of average-derivative quantile regression under the additive model. The techniques are illustrated by a simulated example and a real data set.     

带测量误差的分位数回归模型的参数估计研究

近年来,研究预测变量带测量误差的分位数回归模型的参数估计问题已逐渐成为统计学中的一大热点问题,但由于带测量误差的分位数回归模型的参数估计十分复杂,所以相关研究很少,而目前的研究主要集中于误差分布为球形对称分布的正交回归法和误差分布自由的校正损失函数法等。在回归误差分布为正态分布的假设下,提出修正因子得分法(CFS),即在因子得分法的基础上进行参数估计,并对估计偏差进行修正得到最终估计;通过模拟研究,比较修正因子得分法相对正交回归估计(H-L估计)的优劣,并对修正因子得分法进行综合评价。     

Bayesian Elastic Net Tobit Quantile Regression

In this article, the problem of parameter estimation and variable selection in the Tobit quantile regression model is considered. A Tobit quantile regression with the elastic net penalty from a Bayesian perspective is proposed. Independent gamma priors are put on the l₁ norm penalty parameters. A novel aspect of the Bayesian elastic net Tobit quantile regression is to treat the hyperparameters of the gamma priors as unknowns and let the data estimate them along with other parameters. A Bayesian Tobit quantile regression with the adaptive elastic net penalty is also proposed. The Gibbs sampling computational technique is adapted to simulate the parameters from the posterior distributions. The proposed methods are demonstrated by both simulated and real data examples.     

Evaluating Value-at-Risk Models via Quantile Regression

This article is concerned with evaluating Value-at-Risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Manganelli (2004) are based on such variables. In this article we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker and Xiao 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series.     

Bayesian Semiparametric Modelling in Quantile Regression

Abstract. We propose a Bayesian semiparametric methodology for quantile regression modelling. In particular, working with parametric quantile regression functions, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed non‐parametric prior probability models allow the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models that allow the error distribution to change non‐parametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets.