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.

Transition Logic Regression Method to Identify Interactions in Binary Longitudinal Data

Logic regression is an adaptive regression method which searches for Boolean (logic) combinations of binary variables that best explain the variability in the outcome, and thus, it reveals interaction effects which are associated with the response. In this study, we extended logic regression to longitudinal data with binary response and proposed “Transition Logic Regression Method” to find interactions related to response. In this method, interaction effects over time were found by Annealing Algorithm with AIC (Akaike Information Criterion) as the score function of the model. Also, first and second orders Markov dependence were allowed to capture the correlation among successive observations of the same individual in longitudinal binary response. Performance of the method was evaluated with simulation study in various conditions. Proposed method was used to find interactions of SNPs and other risk factors related to low HDL over time in data of 329 participants of longitudinal TLGS study.

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].

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).

A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models

This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.

Composite Quantile Regression Estimation for Left Censored Response Longitudinal Data

For left censored response longitudinal data, we propose a composite quantile regression estimator（CQR） of regression parameter. Statistical properties such as consistency and asymptotic normality of CQR are studied under relaxable assumptions of correlation structure of error terms. The performance of CQR is investigated via simulation studies and a real dataset analysis.

Weighted quantile regression for longitudinal data using empirical likelihood

This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood(EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.

Composite Quantile Estimation for Kink Model with Longitudinal Data

Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.

Bayesian Nonlinear Quantile Regression Approach for Longitudinal Ordinal Data

Longitudinal data with ordinal outcomes commonly arise in clinical and social studies,where the purpose of interest is usually quantile curves rather than a simple reference range.In this paper we consider Bayesian nonlinear quantile regression for longitudinal ordinal data through a latent variable.An efficient Metropolis–Hastings within Gibbs algorithm was developed for model fitting.Simulation studies and a real data example are conducted to assess the performance of the proposed method.Results show that the proposed approach performs well.

A Longitudinal Study of the Effects of Family Background Factors on Mathematics Achievements Using Quantile Regression

Quantile regression is gradually emerging as a powerful tool for estimating models of conditional quantile functions, and therefore research in this area has vastly increased in the past two decades. This paper, with the quantile regression technique, is the first comprehensive longitudinal study on mathematics participation data collected in Alberta, Canada. The major advantage of longitudinal study is its capability to separate the so-called cohort and age effects in the context of population studies. One aim of this paper is to study whether the family background factors alter performance on the mathematical achievement of the strongest students in the same way as that of weaker students based on the large longitudinal sample of 2000, 2001 and 2002 mathematics participation longitudinal data set. The interesting findings suggest that there may be differential family background factor effects at different points in the mathematical achievement conditional distribution.

The k Nearest Neighbors Estimator of the M-Regression in Functional Statistics

It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data.To solve the problem of typical observations when the covariates of the nonparametric component are functional,the robust estimates for the regression parameter and regression operator are introduced.The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic.We use thek Nearest Neighbors procedure(kNN)to construct the kernel estimator of the proposed robust model.Under some regularity conditions,we state consistency results for kNN functional estimators,which are uniform in the number of neighbors(UINN).Furthermore,a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach.

两维异质性面板分位数模型的双惩罚回归方法

文章关注系数具有两维异质性结构的面板分位数模型,基于SCAD惩罚函数和MCP惩罚函数提出双惩罚最小加权绝对偏差目标函数,同时进行参数估计和两维异质性结构识别。利用ADMM算法求解目标函数,并使用BIC信息准则通过网格搜索选择最优调节参数。根据蒙特卡洛模拟结果验证了所提方法的有限样本性质,最后使用实际数据检验了其应用效果。研究结果表明:所提出的方法能够准确识别两维异质性结构,并且Post估计量的参数估计精确度接近于Oracle估计量。

Generalized Empirical Likelihood Inference in Semiparametric Regression Model for Longitudinal Data

In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.

Quantile regression for survival data in modern cancer research:expanding statistical tools for precision medicin

Quantile regression links the whole distribution of an outcome to the covariates of interest and has become an important alternative to commonly used regression models.However,the presence of censored data such as survival time,often the main endpoint in cancer studies,has hampered the use of quantile regression techniques because of the incompleteness of data.With the advent of the precision medicine era and availability of high throughput data,quantile regression with high-dimensional predictors has attracted much attention and provided added insight compared to traditional regression approaches.This paper provides a practical guide for using quantile regression for right censored outcome data with covariates of low-or highdimensionality.We frame our discussion using a dataset from the Boston Lung Cancer Survivor Cohort,a hospital-based prospective cohort study,with the goals of broadening the scope of cancer research,maximizing the utility of collected data,and offering useful statistical alternatives.We use quantile regression to identify clinical and molecular predictors,for example CpG methylation sites,associated with high-risk lung cancer patients,for example those with short survival.

Single-Index Quantile Regression with Left Truncated Data

The purpose of this paper is two fold.First,the authors investigate quantile regression(QR)estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed.The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained.Further,by combining the QR loss function and the adaptive LASSO penalization,a variable selection procedure for the index parameter is introduced and its oracle property is established.Second,a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution.Furthermore,confidence regions of the index parameter can be constructed.The finite sample performance of the proposed methods are demonstrated.A real data analysis is also conducted to show the usefulness of the proposed approaches.

中国水资源利用效率及影响因素研究

本文研究中国省际用水效率及影响因素,为节水型社会建设提供参考。采用改进的数据包络分析模型测算2015—2020年各地区用水效率;对比普通最小二乘回归结果,进一步利用分位数回归探究影响因素对不同等级用水效率的影响。结果显示:全国平均用水效率在0.45左右波动,呈现倒“U”型趋势。区域用水效率由高至低依次为东部、中部和西部。自然因素、经济发展水平、可持续利用水平、科技进步、人文素养和企业成本对用水效率具有显著影响。其中,水资源禀赋对低用水效率地区的影响显著,而对中、高用水效率地区的影响并不显著,这与“资源诅咒”假说不同。因此,中国用水效率还有较大提升空间,特别是低用水效率地区的改善空间和可选方法最为丰富。

变系数部分非线性模型的分位数回归估计

研究纵向数据缺失下变系数部分非线性分位数回归模型的估计问题.利用逆概率加权法结合分位数回归给出参数估计和非参估计;在一定条件下,证明了所给估计量的渐近正态性;通过数值模拟,验证了所提方法的有效性.

超高维数据下部分线性可加分位数回归模型的变量选择

在超高维数据中,一方面,协变量的维数可能远远大于样本量,甚至随着样本量以指数级的速度增长;另一方面,超高维数据通常是异质的,协变量对条件分布中心的影响可能与他们对尾部的影响大不相同,甚至会出现重尾以及异常点的复杂情况。文章在协变量维度发散且为超高维的情况下研究了部分线性可加分位数回归模型的变量选择和稳健估计问题。首先,为了实现模型的稀疏性和非参数光滑性,引入了一种非凸Atan双惩罚,并采用分位迭代坐标下降算法来解决所提方法的优化问题。在选择适当正则化参数的情况下,证明了所提双惩罚估计量的理论性质。其次,通过模拟研究对所提方法的性能进行验证。模拟结果表明,所提方法比其他惩罚方法具有更好的表现,尤其是在数据存在重尾的情况下。最后,通过基于癌症筛查病人血液样本数据的实证来验证所提方法的实用性。

非参数固定效应Panel Data模型的分位数回归推断

利用分位数回归方法,讨论了非参数固定效应Panel Data模型的估计和检验问题,得到了参数估计的渐近正态性及收敛速度。同时,建立一个秩得分(rank score)统计量来检验模型的固定效应,并证明了这个统计量渐近服从标准正态分布。

分位回归基于最优去相关得分的子抽样算法

针对海量数据下高维分位回归模型,首先,构造基于去相关得分函数的子抽样算法,以估计感兴趣的低维参数;其次,推导所提估计的极限分布,并根据渐近协方差矩阵求出L-最优准则下的子抽样概率,给出高效的两步算法.模拟和实证分析结果表明,最优子抽样方法显著优于均匀子抽样方法.