Smoothed Empirical Likelihood Inference for Nonlinear Quantile Regression Models with Missing Response

In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.

Double-Penalized Quantile Regression in Partially Linear Models

In this paper, we propose the double-penalized quantile regression estimators in partially linear models. An iterative algorithm is proposed for solving the proposed optimization problem. Some numerical examples illustrate that the finite sample performances of proposed method perform better than the least squares based method with regard to the non-causal selection rate (NSR) and the median of model error (MME) when the error distribution is heavy-tail. Finally, we apply the proposed methodology to analyze the ragweed pollen level dataset.

Composite Quantile Regression for Nonparametric Model with Random Censored Data

The composite quantile regression should provide estimation efficiency gain over a single quantile regression. In this paper, we extend composite quantile regression to nonparametric model with random censored data. The asymptotic normality of the proposed estimator is established. The proposed methods are applied to the lung cancer data. Extensive simulations are reported, showing that the proposed method works well in practical settings.

Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China

This paper studies how the price movements of pork,chicken and egg respond to those of related cost factors in short terms in Chinese market.We employ a linear quantile approach not only to explore potential data heteroscedasticity but also to generate confidence bands for the purpose of price stability study.We then evaluate our models by comparing the prediction intervals generated from the quantile regression models with in-sample and out-of-sample forecasts.Using monthly data from January 2000 to October 2010,we observed these findings：（i） the price changes of cost factors asymmetrically and unequally influence those of the livestock across different quantiles;（ii） the performance of our models is robust and consistent for both in-sample and out-of-sample forecasts;（iii） the confidence intervals generated from 0.05th and 0.95th quantile regression models are good methods to forecast livestock price fluctuation.

Probabilistic Quantile Regression-Based Scour Estimation Considering Foundation Widths and Flood Conditions

Scour has been widely accepted as a key reason for bridge failures.Bridges are susceptible and sensitive to the scour phenomenon,which describes the loss of riverbed sediments around the bridge supports because of flow.The carrying capacity of a deep-water foundation is influenced by the formation of a scour hole,which means that a severe scour can lead to a bridge failure without warning.Most of the current scour predictions are based on deterministic models,while other loads at bridges are usually provided as probabilistic values.To integrate scour factors with other loads in bridge design and research,a quantile regression model was utilized to estimate scour depth.Field data and experimental data from previous studies were collected to build the model.Moreover,scour estimations using the HEC-18 equation and the proposed method were compared.By using the“CCC(Calculate,Confirm,and Check)”procedure,the probabilistic concept could be used to calculate various scour depths with the targeted likelihood according to a specified chance of bridge failure.The study shows that with a sufficiently large and continuously updated database,the proposed model could present reasonable results and provide guidance for scour mitigation.

Quantile Regression Based on Semi-Competing Risks Data

This paper considers quantile regression analysis based on semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. The major interest is the covariate effects on the quantile of the non-terminal event time. Dependent censoring is handled by assuming that the joint distribution of the two event times follows a parametric copula model with unspecified marginal distributions. The technique of inverse probability weighting (IPW) is adopted to adjust for the selection bias. Large-sample properties of the proposed estimator are derived and a model diagnostic procedure is developed to check the adequacy of the model assumption. Simulation results show that the proposed estimator performs well. For illustrative purposes, our method is applied to analyze the bone marrow transplant data in [1].

Jackknife Model Averaging for Composite Quantile Regression

In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters.Different from the traditional model averaging for quantile regression which considers only a single quantile,the proposed model averaging estimator is based on multiple quantiles.The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights.The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error.Simulation studies are conducted to demonstrate the finite sample performance of the new model averaging estimator.The proposed method is also applied to the analysis of the stock returns data and the wage data.

Jackknife Model Averaging for Quantile Single-Index Coefficient Model

In the past two decades,model averaging,as a way to solve model uncertainty,has attracted more and more attention.In this paper,the authors propose a jackknife model averaging(JMA) method for the quantile single-index coefficient model,which is widely used in statistics.Under model misspecification,the model averaging estimator is proved to be asymptotically optimal in terms of minimizing out-of-sample quantile loss.Simulation experiments are conducted to compare the JMA method with several model selections and model averaging methods,and the results show that the proposed method has a satisfactory performance.The method is also applied to a real dataset.

Quantile Regression of Ultra-high Dimensional Partially Linear Varying-coefficient Model with Missing Observations

In this paper,we focus on the partially linear varying-coefficient quantile regression with missing observations under ultra-high dimension,where the missing observations include either responses or covariates or the responses and part of the covariates are missing at random,and the ultra-high dimension implies that the dimension of parameter is much larger than sample size.Based on the B-spline method for the varying coefficient functions,we study the consistency of the oracle estimator which is obtained only using active covariates whose coefficients are nonzero.At the same time,we discuss the asymptotic normality of the oracle estimator for the linear parameter.Note that the active covariates are unknown in practice,non-convex penalized estimator is investigated for simultaneous variable selection and estimation,whose oracle property is also established.Finite sample behavior of the proposed methods is investigated via simulations and real data analysis.

An analysis of single-index model with monotonic link function

The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h（.）. Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.

L1/2 -Regularized Quantile Method for Sparse Phase Retrieval

The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L1/2-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.

黄河流域生态环境质量时空演变及驱动力分析

开展黄河流域生态环境质量时空格局演变及驱动因素研究,为黄河流域生态文明建设和人地和谐发展提供科学决策支持。基于2000-2022年的MODIS数据,利用遥感生态指数(RSEI)评估黄河流域生态环境质量,采用Sen趋势分析法和MK检验全面刻画RSEI的空间演变特征。结合分位数回归模型和残差分析探究自然环境和人类活动对不同分位数RSEI变化的影响机制及相对贡献率。结果表明:2000-2022年,黄河流域RSEI年均值为0.465,年均增速为0.55%。黄河流域中游RSEI上升最为显著。流域RSEI改善的区域面积占比为74.94%,显著改善的区域为内蒙古中部及晋陕两省北部地区。同一因素对不同分位数RSEI的影响效应存在显著分异。随着RSEI分位点的提高,温度、降水及高程等3个变量影响程度均呈下降趋势。自然环境和人类活动共同作用导致黄河流域RSEI变化面积占比为64.00%,由人类活动导致RSEI变化的区域面积占比为20.62%,由自然环境导致RSEI变化的区域面积占比为15.38%。

Hierarchical linear regression models for conditional quantiles

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models,but it cannot deal effectively with the data with a hierarchical structure.In practice,the existence of such data hierarchies is neither accidental nor ignorable,it is a common phenomenon.To ignore this hierarchical data structure risks overlooking the importance of group effects,and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid.On the other hand,the hierarchical models take a hierarchical data structure into account and have also many applications in statistics,ranging from overdispersion to constructing min-max estimators.However,the hierarchical models are virtually the mean regression,therefore,they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates.Furthermore,the estimated coefficient vector (marginal effects)is sensitive to an outlier observation on the dependent variable.In this article,a new approach,which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models,is developed.On the theoretical front,we also consider the asymptotic properties of the new method,obtaining the simple conditions for an n1/2-convergence and an asymptotic normality.We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.

基于改进INFO-CNN-QRGRU模型的农村分布式光伏发电短期概率预测

随着“双碳”目标的推进,清洁能源所占比重大幅度增加,分布式光伏发电在我国农村地区快速发展,但其随机性、间歇性的特点给新能源消纳和电网稳定带来很大的挑战。光伏发电预测可以在一定程度上改善新能源消纳问题,减少光伏发电的不稳定性对电网的冲击。因此,为提高光伏发电功率预测精度,提出一种基于改进向量加权平均算法优化CNN-QRGRU网络的光伏发电概率预测方法。首先采用ReliefF算法对特征变量进行选择,在此基础上利用高斯混合模型(Gaussian mixture model,GMM)聚类方法将天气分为晴天、晴转多云和阴雨天3种类型,将处理好的数据输入到CNN-GRU模型中,并利用向量加权平均(weighted mean of vectors algorithm,INFO)优化算法对模型超参数进行调参,将分位数回归模型(quantile regression,QR)与INFO-CNN-GRU模型相结合得到光伏功率条件分布,结合核密度估计法从条件分布中获得概率密度函数,完成概率预测。以实际光伏电站数据作为基础,将提出的INFO优化算法与其他几种传统的优化算法进行对比,结果表明INFO的优化效果更好,在此基础上进行概率预测,得到的概率预测结果相较于点预测能提供更多有效信息,更具有应用价值。

考虑异质交通流的随机参数优化速度跟驰模型

为分析交通流异质性对车辆跟驰行为的影响,基于随机参数线性回归方法改进优化速度函数.根据分位数回归对交通流速度-密度数据进行分类,对每个类别数据进行随机参数线性回归,并得到不同类别的改进优化速度函数与假设检验结果,结合改进的优化速度函数和全速度差跟驰模型建立随机优化速度跟驰模型,利用傅里叶变化理论对跟驰模型进行稳定性分析,并搭建环形车道仿真平台对跟驰模型进行数值实验.结果表明,分类处理后的随机参数模型误差较未分类降低28%;随机参数跟驰车队的速度值随着0.5分位点车辆的增多而增大;随机参数跟驰模型车队较固定参数跟驰模型车队更能反映交通流异质性对车队的影响.建立的模型能够提高仿真维度,真实反映交通流的复杂运行状况.

基于DPSIR模型的城市旅游经济韧性评价与影响因素——以长三角城市群为例

基于DPSIR模型构建旅游经济韧性指标体系,对2009—2021年长三角城市群旅游经济韧性水平进行测度,并分析其演化特征与影响因素,以期为旅游经济韧性提升提供一定决策依据.结果表明:长三角城市群旅游经济韧性呈现“先升后降”的变化趋势,各城市韧性水平整体上呈上升趋势.韧性较高城市主要分布在中东部地区,各城市旅游经济韧性水平间具有一定空间集聚特征.旅游经济韧性受经济发展水平、经济发展结构、旅游发展速度、游客承载量、教育水平、基础设施和政府干预等因素的综合影响,其中旅游发展速度对旅游经济韧性具有明显负面影响,其他因素均具有显著促进作用.

考虑多前车位置及分位数速度差跟驰模型稳定性分析

为探究交通流特性对车辆跟驰行为的影响,基于分位数回归方法对跟驰模型进行改进,通过稳定性分析方法利用车头间距描述交通拥堵情况。根据分位数回归方法对模型中的优化速度函数进行改进,并将其应用于考虑多前车位置及速度差跟驰模型,使模型可以通过分位点的变换,在仿真过程中模拟不同驾驶风格的车辆。运用傅里叶变换理论推导出该模型的线性稳定性条件,并通过摄动法求得其修正Korteweg-de Vries(mKdV)方程的解,根据车头间距的扭结-反扭结解描述交通拥堵的变化情况。分析对比考虑不同因素的跟驰模型的稳定性临界曲线,为评估改进模型的有效性,搭建环形车道仿真平台并对改进模型进行数值实验。结果表明:在仿真实验中,随着分位点的增加,改进模型达到稳定状态的平均速度逐渐增加,车速分别为9.57、12.58、14.76 m/s;相比原模型,改进模型能够实现更少的位移波动,位移差最小为1.05 m;在混合模型实验中,随着激进驾驶风格车辆数量的增加,改进模型与多速度差模型相比,车队整体的平均速度达到12.42 m/s,位移波动能够达到稳定状态。

新冠肺炎疫情对猪肉价格的影响——基于多期DID模型的考察

以新冠肺炎疫情的突然爆发作为切入点,将疫情爆发地区和未爆发地区视为一次部分省份冲击猪肉价格的准自然试验,采用多期DID模型考察新冠肺炎疫情对猪肉价格的影响,并构建DID-QR模型检验新冠肺炎疫情对猪肉价格的处理效应在不同初始价格增长率和不同制度环境下的表现形式。结果表明,新冠肺炎疫情的爆发导致猪肉价格出现大幅度上涨,平均涨幅约为10%;受疫情影响的猪肉价格呈现上涨、平稳、再上涨、再平稳、下跌的变化趋势,在考察期内仅次月、3月、6月和7月涨幅明显,10月开始出现明显的下降趋势。新冠肺炎疫情的爆发拉大了不同地区猪肉价格水平的差距,且疫情对价格的提升作用在初始农业经济发展水平较低地区和初始经济发展水平较高地区较为明显。为此,政府应根据猪肉价格在不同条件下的异质性,有的放矢的采取平抑措施,并通过建立各产业链环节主体衔接机制和完善公共信息平台的方式,减弱猪肉市场受突发性外部冲击的影响。

Likelihood ratio-type tests in weighted composite quantile regression of DTARCH models

The double-threshold autoregressive conditional heteroscedastic(DTARCH) model is a useful tool to measure and forecast the mean and volatility of an asset return in a financial time series. The DTARCH model can handle situations wherein the conditional mean and conditional variance specifications are piecewise linear based on previous information. In practical applications, it is important to check whether the model has a double threshold for the conditional mean and conditional heteroscedastic variance. In this study, we develop a likelihood ratio test based on the estimated residual error for the hypothesis testing of DTARCH models. We first investigate DTARCH models with restrictions on parameters and propose the unrestricted and restricted weighted composite quantile regression(WCQR) estimation for the model parameters. These estimators can be used to construct the likelihood ratio-type test statistic. We establish the asymptotic results of the WCQR estimators and asymptotic distribution of the proposed test statistics. The finite sample performance of the proposed WCQR estimation and the test statistic is shown to be acceptable and promising using simulation studies. We use two real datasets derived from the Shanghai and Shenzhen Composite Indexes to illustrate the methodology.

数字普惠金融的收入增长与收入差距缩小效应研究——来自新疆的经验证据

文章在城乡二元经济结构、金融发展与收入平等理论分析基础上,利用2011—2020年新疆地州面板数据,借助分位数回归和广义空间模型,研究新疆数字普惠金融对城乡居民收入增长的异质性及差距缩小效应。结果表明:数字普惠金融对于城乡居民收入增长具有异质性,且在不同收入水平的情况下,增长效应有差异;数字普惠金融对城乡收入差距有缩小效应,但是空间溢出效应不显著。分维度研究发现,覆盖广度和使用深度对城乡差距的缩小作用显著,但空间溢出效应均不显著。基于此,提出应加快边疆地区农村数字普惠金融建设规模与速度;合理配置金融资源,增强“一圈一带一群”中心城市对落后地区的辐射作用;加快现代化建设,推进城乡一体化发展。