Penalized inverse probability weighted estimators for weighted rank regression with missing covariates

Abstract

In this article, we study the variable selection and estimation for linear regression models with missing covariates. The proposed estimation method is almost as efficient as the popular least-squares-based estimation method for normal random errors and empirically shown to be much more efficient and robust with respect to heavy tailed errors or outliers in the responses and covariates. To achieve sparsity, a variable selection procedure based on SCAD is proposed to conduct estimation and variable selection simultaneously. The procedure is shown to possess the oracle property. To deal with the covariates missing, we consider the inverse probability weighted estimators for the linear model when the selection probability is known or unknown. It is shown that the estimator by using estimated selection probability has a smaller asymptotic variance than that with true selection probability, thus is more efficient. Therefore, the important Horvitz-Thompson property is verified for penalized rank estimator with the covariates missing in the linear model. Some numerical examples are provided to demonstrate the performance of the estimators.     

Ridge Estimation to the Restricted Linear Model

This article is concerned with the problem of multicollinearity in a linear model with linear restrictions. After introducing a spheral restricted condition, a new restricted ridge estimation method is proposed by minimizing the sum of squared residuals. The property of the new estimator in its superiority over the ordinary restricted least squares estimation is then theoretically analyzed. Furthermore, a sufficient and necessary condition for selecting the ridge parameter k is obtained. To simplify the selection of the ridge parameter, a sufficient condition is also given. Finally, a numerical example demonstrates the merit of the new method in the aspect of solving the multicollinearity over the ordinary restricted least squares estimation.     

The Research on Two Kinds of Restricted Biased Estimators Based on Mean Squared Error Matrix

Sakall?oglu et al. (2001 Sakall?oglu , Kaç?ranlar , Akdeniz ( 2001 ). Mean squared error comparisons of some biased estimators . Commun. Statist. Theor. Meth. 30 : 347 – 361 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) dealt with the comparisons among the ridge estimator, Liu estimator, and iteration estimator. Akdeniz and Erol (2003 Akdeniz , F. , Erol , H. ( 2003 ). Mean squared error matrix comparisons of some biased estimators in linear regression . Commun. Statist. Theor. Meth. 32 : 2389 – 2413 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) have compared the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean squared error sense. In this article, we study the ridge estimator and Liu estimator with respect to linear equality restriction, and establish some sufficient conditions for the superiority of the restricted ridge estimator over the restricted Liu estimator and the superiority of the restricted Liu estimator over the restricted ridge estimator under mean squared error matrix, respectively. Furthermore, we give a numerical example.     

A brief proof on the generalized variance bound of the relative efficiency in statistics

In this paper, we obtain a brief proof on the generalized varance bound of the relative efficiency that was simultaneously given by Bloomfield and Watson(1975) and by Knott (1975).     

我国商业银行无形资产统计问题研究

摘　　要:商业银行无形资产是形成商业银行核心竞争力的基础和产生超额收益的源泉,加强商业银行无形资产统计工作,有利于充分揭示商业银行无形资产基本内容和对核心竞争力的影响。笔者认为,目前我国商业银行无形资产统计指标体系设置不完整,统计制度不健全,统计内容不全面,统计分析不深入,影响经济决策。笔者认为,完善商业银行无形资产统计制度时,应从组织结构类、客户关系类、知识创新类和人力资本类等四个方面对无形资产进行统计,逐步细化统计指标,明确具体的统计内容,建立、健全无形资产价值信息系统,深化无形资产统计分析工作,以此为基础,提出提高商业银行核心竞争力的基本策略。     

Ⅱ—32A的配对提纯及其纯系的性状表现

介绍了水稻不育系Ⅱ—32A的提纯经过、方法以及纯系Ⅱ—32—5A、Ⅱ—32—8A的品系纯度不育株率、不育度和生育特性等性状表现。     

浅谈高校英语教师所应具备的素质

精读课是英语专业学生的一门主修课.精读教师的素质对教学质量以及大学生素质的培养起着关键性的作用.本文从精度课角度简单分析了高校英语教师应具备的素质--能力素质和思想道德素质.     

新中国成立前后毛泽东的执政思想与实践

新中国成立前后,毛泽东的执政思想和实践,是中国共产党执政思想的重要组成部分,也是第一代中央领导集体智慧的结晶。这些执政思想和实践,对于加强党的执政能力建设,提高党的执政水平,具有十分重要的现实意义。     

我国国家审计模式重构的探讨

我国的国家审计属于典型的行政模式 ,即各级审计机关隶属于各级政府的行政系统 ,地方各级审计机关受双重领导。随着政治经济体制改革的深入 ,现有的审计模式在许多方面都阻碍了审计机关职能的行使和审计目标的实现 ,审计独立性得不到充分保证 ,因此 ,本文试针对现行审计模式的缺陷 ,对我国国家审计模式提出了新的构想     

制备条件对磷脂酰胆碱单分子膜相变行为的影响

目的:全面探讨制备条件对LB膜相变行为的影响可获得试验室特定设备及条件下制备磷脂LB膜的最佳条件。方法:用热力学相变理论类比描述了单分子膜的相变过程理论,并通过该理论,以π-A曲线和相变过程为主要分析点,系统地研究了磷脂铺展量、铺展浓度、铺展溶剂、铺展时间、压膜速度、亚相温度、亚相pH值等七大因素对成膜质量的影响。结果:磷脂铺展量、亚相的温度和pH值对磷脂单分子膜的质量影响最大,铺展浓度、铺展溶剂、铺展时间的影响要小得多,而在一定范围内压膜速度的大小基本上不影响膜的质量。结论:50μL,0.67mmol/ml的磷脂/乙醚溶液在pH6.8的亚相上铺展20min并以5mm/min的速度挤压单分子膜可获得完整的π-A曲线。