线性模型中回归分位数估计的强相合性

考虑线性系统模型 y=x＇β_0 x＇r_0e, (1)其中x为P维已知向量,β_0是未知的P维回归系数,e是1维不可观察的误差随机变量。 y在x下的条件u分位数可以写成:     

单位根模型的复合分位数自回归推断

单位根模型是经济学和金融学中用于非平稳时间序列数据建模的一个重要模型.对于该模型,假设模型误差的方差可能不存在,然后采用复合分位数方法估计该模型的自回归系数,建立了估计量的收敛速度和极限分布.然后,通过Monte Carlo模拟评估估计量在有限样本情形下的表现发现,当模型误差不是高斯分布时,单位根模型的复合分位数自回归估计在估计偏差和有效性方面要优于最小二乘估计和分位数自回归估计.此外,文中给出了一个相关的实证分析,该实证分析表明:对于该经济数据,用复合分位数方法进行统计推断是合适且具有一定优势的.最后,把单位根模型推广到了增广的Dickey-Fuller模型,并研究了该模型中的复合分位数自回归估计的渐近理论.     

生长曲线模型的分位数回归

生长曲线模型有着广泛的应用, 在经济学、生物学、医学等各个领域的研究都起着重要的作用. 已有文献关于生长曲线模型参数矩阵的估计基本上是使用最小二乘方法或极大似然方法. 使用最小二乘方法, 当误差项服从偏峰分布、厚尾分布、或者存在异常点时, 得出的估计不是有效的; 使用极大似然方法, 要求分布已知, 实际使用时很难满足这一点. 分位数回归能弥补如上这些缺陷, 所得估计具有很好的稳健性. 本文使用分位数回归方法给出生长曲线模型参数矩阵的估计, 及其渐近正态性.     

面板数据分位数回归模型的工具变量估计

针对含有内生变量的面板数据回归模型,提出基于工具变量的分位数回归估计方法.首先,通过引入工具变量解决协变量的内生性问题,然后利用分位数回归的方法对回归系数进行估计.在一些正则条件下,证明所提出估计的大样本性质,通过模拟研究证实该方法的有限样本性质.     

基于Copula分位数回归原油期货市场套保模型及效率研究

伴随中国原油期货的上市,作为商品期货最大交易单品的原油期货,其套期保值功能必将成为新的研究热点。本文采用skew-t-GARCH(1,1)模型捕捉原油期现货收益率的"波动集聚"和"尖峰厚尾"特性,在此基础上通过构造Copula分位数套保模型研究不同原油市场状态下(牛市、熊市)的套保比率及效率。利用蒙特卡洛模拟对线性、Normal Copula及T-Copula分位数回归模型进行效率比较,并对英国Brent和美国WTI原油期货收益率进行实证研究,结果表明:①不同市场状态下,原油期货的最优套保比率具有非对称性;②T-Copula分位数回归模型的尾部套期保值效率更稳定。因此,利用原油期货进行规避风险时,要根据市场行情合理运用套期保值模型。     

估计极端行为模型:分位数回归方法及其实现与应用

在许多社会和管理研究中,研究者通常很感兴趣不同于期望或平均的极端行为的理论解释。这些特殊个案所包含的信息往往是研究的创新点和解决某些问题的突破口,但传统的最小平方法与最小一乘法并不适宜于这类研究问题的解决。本文讨论一种估计极端行为的理想模型:分位数回归。本文在对分位数回归的国内外研究现状进行综述后,介绍了分位数回归的模型和实现方法,并将它与最小平方法、最小一乘法进行了比较。最后探讨它在我国管理研究领域的应用方式和有关条件。     

复合分位数下门限自回归模型的变点估计

金融领域中的突发事件是变点问题的一种体现,往往由于其随机性和发生前信息量不足等因素造成突发事件难以识别和预测.金融市场常常表现出非线性和异质性等特征,门限分位数自回归模型作为金融领域变点问题研究的重要模型,逐渐在经济和统计学界获得更多的关注.本文结合不同的分位数对门限分位数自回归模型中的交点估计问题提出两种新的估计方法...     

零调整分位数回归模型在车辆保险索赔额中的研究与应用

车辆保险产品的定价一般会考虑保单持有人的索赔概率和期望索赔额等两个因素,零调整逆高斯回归模型作为解决这类问题的一个有力工具,由于变量分布的限定,从而具有一定的局限性.针对该问题,本文基于零调整逆高斯回归模型和分位数回归模型的思想,提出零调整分位数回归模型,并结合实际数据进行了拟合分析.与零调整逆高斯回归模型拟合的结果比较表明,零调整分位数回归模型可以作为研究车辆保险中索赔额的一个有力工具.     

基于神经网络分位数回归的多期CVaR风险测度

与VaR金融风险测度相比,CVaR具有更好的数理性质,其计算方法成为关注的焦点。相对于单期CVaR而言,多期CVaR风险测度具有较强的非线性特征,其建模过程更加复杂。在神经网络分位数回归基础上,建立了一种新的多期CVaR风险测度方法;基于似然比检验,建立了多期CVaR风险测度返回测试评价准则。将该新方法应用于沪深300指数的多期CVaR风险测度,并将其与传统的测度方法进行了对比,返回测试结果表明:第一,该新方法具有较强的稳健性,各期平均绝对误差大小基本不变,特别适合于多期CVaR风险测度;第二,基于神经网络分位数回归的多期CVaR风险测度效果优于传统测度方法,表现为似然比检验拒绝次数最少和平均绝对误差最小。     

分组数据分位数回归模型的变量选择和估计北大核心CSCD

本文主要研究分组数据分位数回归模型的变量选择和估计问题.为了充分反映数据的分组信息,需要假定每组数据的回归系数可以分解成共性部分和分组后的个性部分.为了进行变量筛选,本文提出分解系数的Lasso估计,并进一步提出了自适应Lasso估计.在处理相应优化问题时,采用了变换观测矩阵的方法简化问题求解.本文给出了自适应Lasso估计的Oracle性质证明,并且通过数值模拟研究展示了所提方法的有限样本表现.最后,将此方法应用到乳腺浸润癌致病基因的变量筛选上来展示所提方法的实际应用表现.     

Estimation and test procedures for composite quantile regression with covariates missing at random

In this paper, we study the weighted composite quantile regression (WCQR) for general linear model with missing covariates. We propose the WCQR estimation and bootstrap test procedures for unknown parameters. Simulation studies and a real data analysis are conducted to examine the finite performance of our proposed methods.     

Partial functional linear quantile regression

This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optimal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also be established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.     

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 method outperforms most other existing methods in the sense of the mean square estimation (MSE) and mean absolute estimation (MAE) criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.     

Composite hierachical linear quantile regression

Multilevel （hierarchical） modeling is a generalization of linear and generalized linear modeling in which regression coefficients are modeled through a model, whose parameters are also estimated from data. Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance （like Cauchy distribution） tends to infinity. This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression, which greatly improves the efficiency and precision of the estimation. The new approach, which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models, still works well when the error variance tends to infinity, We show that even the error distribution is normal, the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression. When the error distribution is not normal, our method still enjoys great advantages in terms of estimation efficiency.     

删失分位数回归模型基于扩展兴趣信息准则的平均估计

本文结合分位数回归技术,基于删失回归模型,把Claeskens和Hjort的传统兴趣信息准侧(focused information criterion,FIC)扩展到兴趣向量的情形,提出扩展的兴趣信息准则(extended focused information criterion,E-FIC),有效解决了同时针对多个兴趣参数的平均估计问题,并且对删失响应变量的不同水平分位数进行建模,以全面反映响应变量分布特征,有效克服异常值和厚尾模型误差的影响.基于扩展的兴趣信息准则给出参数的平均估计方法,证明估计的渐近性质.通过Monte Carlo随机模拟试验比较所提估计方法和最小二乘方法在有限样本量下的表现,用所提方法对原发性胆汁性肝硬化数据集进行数据分析.     

左截断数据下非参数回归模型的复合分位数回归估计

利用局部多项式方法研究了误差具有异方差结构的非参数回归模型,在左截断数据下构造了回归函数的复合分位数回归估计,并得到了该估计的渐近正态性结果,最后通过模拟,在服从一些非正态分布的误差下,得到该估计比局部线性估计更有效.     

Weighted composite quantile estimation and variable selection method for censored regression model

This paper considers the weighted composite quantile (WCQ) regression for linear model with random censoring. The adaptive penalized procedure for variable selection in this model is proposed, and the consistency, asymptotic normality and oracle property of the resulting estimators are also derived. The simulation studies and the analysis of an acute myocardial infarction data set are conducted to illustrate the finite sample performance of the proposed method.     

Simple outlier labeling based on quantile regression,with application to the steelmaking process

This paper introduces some methods for outlier identification in the regression setting, motivated by the analysis of steelmaking process data. The proposed methodology extends to the regression setting the boxplot rule, commonly used for outlier screening with univariate data. The focus here is on bivariate settings with a single covariate, but extensions are possible. The proposal is based on quantile regression, including an additional transformation parameter for selecting the best scale for linearity of the conditional quantiles. The resulting method is used to perform effective labeling of potential outliers, with a quite low computational complexity, allowing for simple implementation within statistical software as well as commonly used spreadsheets. Some simulation experiments have been carried out to study the swamping and masking properties of the proposal. The methodology is also illustrated by some real life examples, taking as the response variable the energy consumed in the melting process. Copyright © 2015 John Wiley & Sons, Ltd.     

Consistency of kernel‐based quantile regression

Quantile regression is used in many areas of applied research and business. Examples are actuarial, financial or biometrical applications. We show that a non‐parametric generalization of quantile regression based on kernels shares with support vector machines the property of consistency to the Bayes risk. We further use this consistency to prove that the non‐parametric generalization approximates the conditional quantile function which gives the mathematical justification for kernel‐based quantile regression. Copyright © 2008 John Wiley & Sons, Ltd.     

Value-at-Risk with quantile regression neural network: New evidence from internet finance firms

Traditional risk measurements have proven inadequate in capturing tail risk and nonlinear correlation. This study proposes a novel approach to measure financial risk in the Internet finance industry: a new Value-at-Risk (VaR) measurement based on quantile regression neural network (QRNN). Sparrow Search Algorithm (SSA) is utilized to optimize the QRNN model, which improves the model's performance in predicting internet finance risk. By comparing the TGARCH-VaR and QR-VaR approaches, our study demonstrates the effectiveness of the QRNN-VaR approach and its potential to improve the accuracy of risk prediction in the Internet finance industry. This study further examines and compares the risks between the traditional and internet finance industries. It also considers the unique impact of COVID-19 on industry risk based on statistical testing for differences and machine learning models. Our results indicate that the level of risk in the Internet finance industry is higher than in the traditional finance industry. Moreover, COVID-19 has contributed to increased risk within the Internet finance industry. These findings have significant implications for investors and policymakers seeking to better understand and manage risks within the Internet finance industry, particularly in the ongoing COVID-19 pandemic.