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缺失数据下超高维可加分位回归的变量筛选和选择

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数学学报（中文版） 2024年第3期67卷 444-467页

作者：白永昕钱曼玲田茂再北京信息科技大学理学院北京100192 墨尔本大学数学与统计学院澳大利亚墨尔本3010 中国人民大学应用统计科学研究中心、中国人民大学统计学院北京100872 新疆财经大学新疆社会经济统计研究中心、新疆财经大学统计与信息学院乌鲁木齐830012 新疆医科大学医学工程技术学院乌鲁木齐830063

针对存在缺失数据的超高维可加分位回归模型,本文提出一种有效的变量筛选方法.具体而言,将典型相关分析的思想引入到最优变换的最大相关系数,通过协变量和模型残差最优变换后的最大相关系数重要变量的边际贡献进行排序,从而进行变量筛选... 详细信息

针对存在缺失数据的超高维可加分位回归模型,本文提出一种有效的变量筛选方法.具体而言,将典型相关分析的思想引入到最优变换的最大相关系数,通过协变量和模型残差最优变换后的最大相关系数重要变量的边际贡献进行排序,从而进行变量筛选.然后,在筛选的基础上,利用稀疏光滑惩罚进一步做变量选择.所提变量筛选方法有三点优势:(1)基于最优变换的最大相关可以更全面的反映响应变量对协变量的非线性依赖结构;(2)在迭代过程中利用残差可以获取模型的相关信息,从而提高变量筛选的准确度;(3)变量筛选过程和模型估计分开,可以避免对冗余协变量的回归.在适当的条件下,证明了变量筛选方法的确定性独立筛选性质以及稀疏光滑惩罚下估计量的稀疏性和相合性.同时,通过蒙特卡罗模拟给出了所提方法的表现并通过一组小鼠基因数据说明了所提方法的有效性.

关键词：可加分位回归变量筛选稀疏光滑惩罚

Adaptive Local Linear Quantile Regression

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Acta Mathematicae Applicatae Sinica 2011年第3期27卷 509-516页

作者： Yu-nan Su mao-zai tian Center for Applied Statistics School of Statistics Remin University of China Beijing 100872 China

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.

关键词： quantile regression local linear regression adaptive smoothing automatic choice of window size Robustness

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

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Acta Mathematicae Applicatae Sinica 2008年第1期24卷 85-98页

作者： Xi-zhi Wu mao-zai tian Center for Applied Statistics School of Statistics Renmin University of China Beijing 100872 China School of Statistics Renmin University of China Beijing 100872 China

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.

关键词： Mathematical achievement family background factors quantile regression confidence intervals,longitudinal study

A New Generalized Linear Exponential Distribution and Its Applications

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Acta Mathematicae Applicatae Sinica 2014年第4期30卷 1049-1062页

作者： Yu-zhu tian mao-zai tian Qian-qian ZHU School of Mathematics and Information Science Henan Polytechnic University Center for Applied Statistics School of StatisticsRenmin University of China School of Statistics Lanzhou University of Finance and Economics

A new generalized linear exponential distribution （NCLED） is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations （MLE） of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.

关键词： generalized linear exponential distribution (GLED) linear exponential distribution Hazard ratefunction maximum likelihood estimation (MLE)

Momentum Effect Differs Across Stock Performances:Chinese Evidence

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 279-288页

作者： Zhao-yuan LI Si-bo LIU mao-zai tian Department of Statistics and Actuarial Science The University of Hong Kong Department of Finance and Insurance Lingnan University Center for Applied Statistics School of StatisticsRenmin University of China School of Statistics Lanzhou University of Finance and Economics

Prior empirical studies find positive and negative momentum effect across the global nations, but few focus on explaining the mixed results. In order to address this issue, we apply the quantile regression approach to analyze the momentum effect in the context of Chinese stock market in this paper. The evidence suggests that the momentum effect in Chinese stock is not stable across firms with different levels of performance. We find that negative momentum effect in the short and medium horizon （3 months and 9 months） increases with the quantile of stock returns. And the positive momentum effect is observed in the long horizon （12 months）, which also intensifies for the high performing stocks. According to our study, momentum effect needs to be examined on the basis of stock returns. OLS estimation, which gives an exclusive and biased result, provides misguiding intuitions for momentum effect across the global nations. Based on the empirical results of quantile regression, effective risk control strategies can also be inspired by adjusting the proportion of assets with past performances.

关键词： chinese stock market investment strategy momentum effect quantile regression

Semiparametric Quantile Modelling of Hierarchical Data

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Acta Mathematica Sinica,English Series 2009年第4期25卷 597-616页

作者： mao zai tian Man Lai TANG Ping Shing CHAN School of Statistics Renmin University of China Beijing 100872 P. R. China Center for Applied Statistics Renmin University of China Beijing 100872 P. R. China Department of Mathematics Hong Kong Baptist University Kowloon Hong Kong Department of Statistics The Chinese University of Hong Kong Shatin N.T. Hong Kong

The classic hierarchical linear model formulation provides a considerable flexibility for modelling the random effects structure and a powerful tool for analyzing nested data that arise in various areas such as biology, economics and education. However, it assumes the within-group errors to be independently and identically distributed （i.i.d.） and models at all levels to be linear. Most importantly, traditional hierarchical models （just like other ordinary mean regression methods） cannot characterize the entire conditional distribution of a dependent variable given a set of covariates and fail to yield robust estimators. In this article, we relax the aforementioned and normality assumptions, and develop a so-called Hierarchical Semiparametric Quantile Regression Models in which the within-group errors could be heteroscedastic and models at some levels are allowed to be nonparametric. We present the ideas with a 2-level model. The level-1 model is specified as a nonparametric model whereas level-2 model is set as a parametric model. Under the proposed semiparametric setting the vector of partial derivatives of the nonparametric function in level-1 becomes the response variable vector in level 2. The proposed method allows us to model the fixed effects in the innermost level （i.e., level 2） as a function of the covariates instead of a constant effect. We outline some mild regularity conditions required for convergence and asymptotic normality for our estimators. We illustrate our methodology with a real hierarchical data set from a laboratory study and some simulation studies.

关键词： hierarchical models quantile regression robustness

Kernel Quantile Estimator with ICI Adaptive Bandwidth Selection Technique

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Acta Mathematica Sinica,English Series 2014年第4期30卷 710-722页

作者： Jie Yu FAN Man Lai TANG mao zai tian Department of Statistics University of Pittsburgh Department of Mathematics and Statistics Hang Seng Management College School of Statistics Lanzhou University of Finance and Economics Center for Applied Statistics School of StatisticsRenmin University of China

In this article, we consider a class of kernel quantile estimators which is the linear combi- nation of order statistics. This class of kernel quantile estimators can be regarded as an extension of some existing estimators. The exact mean square error expression for this class of estimators will be provided when data are uniformly distributed. The implementation of these estimators depends mostly on the bandwidth selection. We then develop an adaptive method for bandwidth selection based on the intersection confidence intervals （ICI） principle. Monte Carlo studies demonstrate that our proposed approach is comparatively remarkable. We illustrate our method with a real data set.

关键词： Adaptive bandwidth selection ICI principle kernel estimator quantiles

The Analysis of Impact of Brexit on the Post-Brexit EU Using Intervented Multivariate Time Series

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Acta Mathematicae Applicatae Sinica 2021年第3期37卷 441-458页

作者： Yu tian Shao-pei MA Rong-xiang RUI Zhen YU mao-zai tian Institute for Diplomacy and International Governance Loughborough University LondonE203BSUK Center for Applied Statistics School of StatisticsRenmin University of ChinaBeijing 100872China College of Medical Engineering and Technology Xinjiang Medical UniversityUrumqi 830011China School of Statistics and Data Science Xinjiang University of Finance and EconomicsUrumqi 830012China School of Statistics Lanzhou University of Finance and EconomicsLanzhou 730101China

The UK is the most important partner of the EU in terms of economic and other fields due to the geographical *** was one of the largest economies in the EU and its per capita income is higher than the EU average,so it is a net contributor to the *** UKs membership of the EU ended on 31 January 2019,there are concerns that the Brexit may have a significant impact on the EU,resulting in social,economic,political,and institutional changes,*** *** the impact of Brexit on the UK has always been the subject of considerable scholarly interest in recent years,there is relatively little literature on the impact of Brexit on the *** paper focuses on the evaluation of the impact of Brexit on the EU economy and other relevant aspects along three dimensions:GDP,PPP,Quarterly GDP *** powerful quantitative analysis technology that includes vector autoregression model,multivariate time series model with intervention variables,and autoregression integrated moving average,this paper obtains the important and novel evidence about the potential impact of Brexit on the EU economy,pointing out that Brexit is of far-reaching significance to the *** analysis uses several statistical models to screen out several key influencing factors,which can be used to predict the total GDP of EU in the next five *** results show that EU economy will react negatively to"no-deal"Brexit,and its growth rate of economy will slow down significantly in next 5 ***,we put forward relevant policy suggestions on how to deal with the negative impact of Brexit on EU.

关键词： intervention multivariate time series model Brexit economy gaping Brexit hole no-deal Brexit post-Brexit EU

Simultaneous Estimation of Multiple Conditional Regression Quantiles

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 448-457页

作者： Yan-ke WU Ya-nan HU Jian ZHOU mao-zai tian Faculty of Mathematics and Computer Science Guangdong Ocean UniversityZhanjiang 524088China Center for Applied Statistics School of StatisticsRenmin University of ChinaBeijing 100872China School of Statistics Lanzhou University of Finance and EconomicsLanzhou 730101China School of Statistics and Information Xinjiang University of Finance and EconomicsUrumqi 830012China Business School Zhengzhou UniversityZhenzhou 450001China China Academy of Transportation Sciences Beijing 100029China

In this article, we put forward a new approach to estimate multiple conditional regression quantiles simultaneously. Unlike the double summation method in most of the literatures, our proposed model allows continuous variety for the quantile level over(0,1). As a result, all the quantile curves can be obtained via a 2-dimensional surface simultaneously. Most importantly, the proposed minimizing criterion can be readily transformed to a linear programming problem. We use tensor product bi-linear quantile smoothing B-splines tofit it. The asymptotic property of the estimator is derived and a real data set is analyzed to demonstrate the proposed method.

关键词： Simultaneous Estimation Conditional Regression Quantiles B-spline Tensor Product