删失数据下单指标模型的经验似然推断

考虑删失数据下单指标模型, 研究了模型中参数的经验似然推断, 证明了所提出的调整的经验对数似然比渐近于卡方分布, 由此构造相应兴趣参数的置信域. 进一步, 由于模型中参数向量的范数等于1,利用该约束条件来降低参数的维数, 从而增加置信域的精度.模拟研究比较了经验似然方法和正态逼近方法的有限样本性质,从置信域的面积和覆盖概率两方面进行了比较,模拟结果表明经验似然方法优于正态逼近方法.     

核实数据下非线性EV模型中经验似然降维推断

本文研究了响应变量有误差的非线性模型.应用半参数降维技术构造未知参数的被估计经验似然及调整的经验似然,证明了所提出的被估计的经验对数似然与其调整的经验对数似然分别渐近于独立卡方变量加权和的分布与标准卡方分布,所得结果可用来构造未知参数的置信域.     

随机右删失数据下半参数线性变换模型的经验似然推断

本文研究了响应变量随机右删失情形下半参数线性变换模型的经验似然推断问题.构造了参数的经验似然比检验统计量,证明了经验似然比检验统计量的渐近分布为加权卡方分布.在此基础上,对经验似然比检验统计量进行了调整,证明了调整的经验似然比检验统计量的渐近分布为标准的卡方分布.基于经验似然和调整的经验似然方法,分别给出了回归参数的一定置信水平的置信域.最后对本文的方法和传统的正态逼近方法进行了模拟比较,模拟结果显示,从置信域的大小和经验覆盖概率两个角度看,本文的方法均比正态逼近方法优越.     

随机右删失数据下半参数线性变换模型的经验似然推断北大核心CSCD

本文研究了响应变量随机右删失情形下半参数线性变换模型的经验似然推断问题.构造了参数的经验似然比检验统计量,证明了经验似然比检验统计量的渐近分布为加权卡方分布.在此基础上,对经验似然比检验统计量进行了调整,证明了调整的经验似然比检验统计量的渐近分布为标准的卡方分布.基于经验似然和调整的经验似然方法,分别给出了回归参数的一定置信水平的置信域.最后对本文的方法和传统的正态逼近方法进行了模拟比较,模拟结果显示,从置信域的大小和经验覆盖概率两个角度看,本文的方法均比正态逼近方法优越.     

Panel Count Data模型参数的经验似然推断

对Panel Count Data的处理越来越受到人们的关注,Sun与Wei^([1-2])基于简单的半参数模型,提出了Panel Count Data的回归分析,并且给出了参数的估计方程。本文则基于经验似然的思想,讨论了上述Panel Count Data模型参数的置信域构造问题,特别仅通过经验似然置信区域给出了参数估计的方差阵估计,证明了估计的1/n相合性。基于Sun与Wei所给的数据,给出了参数置信区域的具体构造过程和结果。通过作图比较可以看出经验似然置信域要优于依据渐近正态性所构造的置信域。我们还依据所作出的经验似然置信域对参数估计的方差矩阵进行了估计,与用传统渐近正态性得到的矩阵较为接近。     

部分函数线性模型的经验似然推断

本文考虑部分函数线性回归模型,研究了回归系数的经验似然推断,证明了所提出的经验对数似然比渐近于χ~2分布,此结果可以用来构造了相应兴趣参数的置信域.另外,本文也给出了系数函数的极大经验似然估计,并在适当条件下给出了所提出估计量的收敛速度.仅就置信域精度及其覆盖概率大小方面,通过模拟研究和实例分析比较了经验似然方法与最小二乘方法的优劣.     

右删失数据下非线性回归模型的经验似然推断

考虑随机右删失数据下非线性回归模型,提出了模型中未知参数的调整的经验对数似然比统计量.在一定的条件下,证明了.所提出的的统计量具有渐近χ~2分布,由此结果构造了兴趣参数的置信域.通过模拟研究,对经典的经验似然、调整的经验似然和非线性最小二乘方法在有限样本下进行了比较,并对氯离子浓度试验数据进行了分析.     

协变量随机缺失下线性模型的经验似然推断及其应用

考虑协变量带有缺失的线性模型,提出了加权的经验似然方法和借补的经验似然方法,证明了所提出的经验对数似然比渐近于χ~2分布,由此构造回归系数的置信域。模拟研究了所提出方法的有限样本性质,并进行了实例分析。     

纵向数据下部分非线性模型的广义经验似然推断

本文研究了纵向数据下部分非线性模型中未知参数的置信域的构造.利用经验似然方法,构造了非线性函数中未知参数的广义对数经验似然比统计量,证明了其渐近于卡方分布.同时,得到了未知参数的最大经验似然估计,并证明了其渐近正态性.     

带有缺失数据的非线性误差模型中参数的置信域

考虑协变量有测量误差且响应变量随机缺失的非线性模型.在条件分布形式已知的情况下,通过借补方法构造了参数的经验似然,提出了基于模拟的经验似然,证明了所构造的统计量都具有渐近x~2分布,所得结果可构造未知参数的置信域.     

缺失数据下线性模型中反映变量均值的经验似然置信区间

在协变量和反映变量都缺失下,构造了线性模型中反映变量均值的经验似然置信区间,数据模拟表明调整的经验似然置信区间有较好的覆盖率和精度,进一步完善了缺失数据下对线性模型的研究.     

随机插补下两线性模型中响应变量分位数差异的经验似然置信区间

设两个样本数据不完全的线性模型,其中协变量的观测值不缺失,响应变量的观测值随机缺失。采用随机回归插补法对响应变量的缺失值进行补足,得到两个线性回归模型的"完全"样本数据,在一定条件下得到两响应变量分位数差异的对数经验似然比统计量的极限分布为加权x_1~2,并利用此结果构造分位数差异的经验似然置信区间。模拟结果表明在随机插补下得到的置信区间具有较高的覆盖精度。     

Empirical likelihood for single-index models

The empirical likelihood method is especially useful for constructing confidence intervals or regions of the parameter of interest. This method has been extensively applied to linear regression and generalized linear regression models. In this paper, the empirical likelihood method for single-index regression models is studied. An estimated empirical log-likelihood approach to construct the confidence region of the regression parameter is developed. An adjusted empirical log-likelihood ratio is proved to be asymptotically standard chi-square. A simulation study indicates that compared with a normal approximation-based approach, the proposed method described herein works better in terms of coverage probabilities and areas (lengths) of confidence regions (intervals).     

核实数据下响应变量缺失的线性EV模型经验似然推断

考虑响应变量随机缺失而协变量带有误差的线性模型,借助于核实数据和借补方法,构造了回归系数的两种经验似然比,证明了所提出的估计的经验对数似然比渐近于一个自由度为1的独立χ2变量的加权和;而经调整后所得的调整经验对数似然比渐近于自由度为p的χ2分布,该结果可以用来构造未知参数的置信域.此外,我们也构造了响应均值的调整经验对数似然比统计量,并证明了所提出的统计量渐近于x2分布,可用此结果构造响应均值的置信域.通过模拟研究比较了置信域的精度及其平均区间长度.     

Empirical Likelihood Semiparametric Regression Analysis under Random Censorship

This paper considers large sample inference for the regression parameter in a partly linear model for right censored data. We introduce an estimated empirical likelihood for the regression parameter and show that its limiting distribution is a mixture of central chi-squared distributions. A Monte Carlo method is proposed to approximate the limiting distribution. This enables one to make empirical likelihood-based inference for the regression parameter. We also develop an adjusted empirical likelihood method which only appeals to standard chi-square tables. Finite sample performance of the proposed methods is illustrated in a simulation study.     

Empirical likelihood inference for a partially linear errors-in-variables model with covariate data missing at random

The authors study the empirical likelihood method for partially linear errors-in-variablesmodel with covariate data missing at random. Empirical likelihood ratios for the regression coefficients and the baseline function are investigated, and the corresponding empirical log-likelihood ratios are proved to be asymptotically standard chi-squared, which can be used to construct confidence regions. The finite sample behavior of the proposed methods is evaluated by a simulation study which indicates that the proposed methods are comparable in terms of coverage probabilities and average length of confidence intervals. Finally, the Earthquake Magnitude dataset is used to illustrate our proposed method.     

Empirical likelihood for linear models with missing responses

The purpose of this article is to use an empirical likelihood method to study the construction of confidence intervals and regions for the parameters of interest in linear regression models with missing response data. A class of empirical likelihood ratios for the parameters of interest are defined such that any of our class of ratios is asymptotically chi-squared. Our approach is to directly calibrate the empirical log-likelihood ratio, and does not need multiplication by an adjustment factor for the original ratio. Also, a class of estimators for the parameters of interest is constructed, and the asymptotic distributions of the proposed estimators are obtained. Our results can be used directly to construct confidence intervals and regions for the parameters of interest. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths/areas of confidence intervals/regions. An example of a real data set is used for illustrating our methods.     

Empirical likelihood inference for censored median regression model via nonparametric kernel estimation

An alternative to the accelerated failure time model is to regress the median of the failure time on the covariates. In the recent years, censored median regression models have been shown to be useful for analyzing a variety of censored survival data with the robustness property. Based on missing information principle, a semiparametric inference procedure for regression parameter has been developed when censoring variable depends on continuous covariate. In order to improve the low coverage accuracy of such procedure, we apply an empirical likelihood ratio method (EL) to the model and derive the limiting distributions of the estimated and adjusted empirical likelihood ratios for the vector of regression parameter. Two kinds of EL confidence regions for the unknown vector of regression parameters are obtained accordingly. We conduct an extensive simulation study to compare the performance of the proposed methods with that normal approximation based method. The simulation results suggest that the EL methods outperform the normal approximation based method in terms of coverage probability. Finally, we make some discussions about our methods.     

缺失数据下半参数回归模型的经验似然推断

针对响应变量缺失下的半参数回归模型,构造模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近χ2分布,由此构造未知参数的置信域,并就置信域的覆盖概率及区间长度方面,通过模拟研究与最小二乘法进行优劣比较.