缺失数据下非线性分位数回归模型的光滑经验似然推断

利用光滑经验似然方法,讨论了缺失数据下非线性分位数回归模型的回归系数的经验似然置信区域。     

鞅差序列误差下线性模型的经验似然推断

文章在线性模型误差项为鞅差序列情形下,应用经验似然方法得到了关于回归系数β的对数经验似然比统计量渐近服从菇分布,从而得到了关于β的置信域。     

缺失数据下均值的经验似然置信区间

文章在数据缺失的情况下用两种不同的数据补足方式得到了"完全样本":进而给出了各自均值的经验似然的置信区间,并通过模拟比较了两种补足方式的优劣.     

带线性误差的部分线性EV模型的经验似然推断

部分线性EV模型是经典的部分线性模型的推广,在此模型中,假定误差是线性过程.文章把经验似然方法推广到带线性误差的部分线性EV模型,提出了调整的经验对数似然比,并建立了非参数的Wilks定理.     

纵向数据下工具变量线性回归模型的经验似然推断

文章考虑纵向数据下工具变量线性回归模型,基于工具变量和二次推断函数方法,提出了回归参数的经验对数似然比统计量.在一些正则条件下,证明了所提出的经验对数似然比统计量渐近于标准卡方分布,由此构造兴趣参数的置信域.     

缺失偏态数据下线性回归模型的统计推断

研究缺失偏态数据下线性回归模型的参数估计问题,针对缺失偏态数据,为克服样本分布扭曲缺点和提高模型的回归系数、尺度参数和偏度参数的估计效果,提出了一种适合偏态数据下线性回归模型中缺失数据的修正回归插补方法.通过随机模拟和实例研究,并与均值插补、回归插补、随机回归插补方法比较,结果表明所提出的修正回归插补方法是有效可行的.     

协变量缺失下非线性分位数回归中参数的经验似然推断

文章考虑协变量缺失下非线性分位数回归中参数部分的经验似然统计推断,提出了加权修正的估计方程,并给出了当缺失机制已知和未知时极大经验似然估计的渐近分布,得到了著名的Horvitz-Thompson现象.     

广义矩和广义经验似然估计量的有限样本性质比较

文章在线性单方程结构模型框架内运用蒙特卡洛模拟技术对广义矩(GMM)和广义经验似然(GEL)估计量的有限样本性质进行了比较.研究发现:虽然GMM和GEL一阶渐近等价,但它们的有限样本性质依赖于可获取的工具变量数、内生性强弱和样本容量:在样本容量较小时使用GEL能有效改善GMM估计偏差.     

广义矩估计的延伸——广义经验似然估计

从广义矩估计(GMM)到广义经验似然估计(GEL)的发展,是由于GMM估计量小样本性质的不足,促使人们寻求方法的改进和拓展。通过必要的证明和推导,详细解析GEL类估计量(包括EL,ET,CUE)的逻辑关系和数理结构,认识GEL的内在本质,并运用随机模拟方法证实了在小样本场合GEL类估计量比GMM估计量具有更小的估计偏差和均方误差,即GEL类估计改进了GMM估计的小样本性质。     

负相协样本下总体分位数的经验似然渐近性质的推断

文章在强平稳负相协样本下,利用分组经验似然比方法,克服了传统经验似然方法的缺陷,所得到的渐近分布为标准的卡方分布,便于构造总体分位数的渐近置信区间.     

Generalized Empirical Likelihood Inference in Generalized Linear Models for Longitudinal Data

In this article, the generalized linear model for longitudinal data is studied. A generalized empirical likelihood method is proposed by combining generalized estimating equations and quadratic inference functions based on the working correlation matrix. It is proved that the proposed generalized empirical likelihood ratios are asymptotically chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. In addition, the maximum empirical likelihood estimates of parameters are obtained, and their asymptotic normalities are proved. Some simulations are undertaken to compare the generalized empirical likelihood and normal approximation-based method in terms of coverage accuracies and average areas/lengths of confidence regions/intervals. An example of a real data is used for illustrating our methods.     

Empirical Likelihood-based Inference in Linear Models with Missing Data

The missing response problem in linear regression is studied. An adjusted empirical likelihood approach to inference on the mean of the response variable is developed. A non-parametric version of Wilks's theorem for the adjusted empirical likelihood is proved, and the corresponding empirical likelihood confidence interval for the mean is constructed. With auxiliary information, an empirical likelihood-based estimator with asymptotic normality is defined and an adjusted empirical log-likelihood function with asymptotic χ² is derived. A simulation study is conducted to compare the adjusted empirical likelihood methods and the normal approximation methods in terms of coverage accuracies and average lengths of the confidence intervals. Based on biases and standard errors, a comparison is also made between the empirical likelihood-based estimator and related estimators by simulation. Our simulation indicates that the adjusted empirical likelihood methods perform competitively and the use of auxiliary information provides improved inferences.     

Empirical Likelihood for Nonparametric Models Under Linear Process Errors

In this paper, we study the construction of confidence intervals for a nonparametric regression function under linear process errors by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically distributed. The result is used to obtain EL based confidence intervals for the nonparametric regression function. The finite‐sample performance of the method is evaluated through a simulation study.     

Empirical Likelihood for Partially Non Linear Models with Missing Response Variables at Random

This article is concerned with partially non linear models when the response variables are missing at random. We examine the empirical likelihood (EL) ratio statistics for unknown parameter in non linear function based on complete-case data, semiparametric regression imputation, and bias-corrected imputation. All the proposed statistics are proven to be asymptotically chi-square distribution under some suitable conditions. Simulation experiments are conducted to compare the finite sample behaviors of the proposed approaches in terms of confidence intervals. It showed that the EL method has advantage compared to the conventional method, and moreover, the imputation technique performs better than the complete-case data.     

Empirical Likelihood for Generalized Partially Linear Single-index Models

Empirical-likelihood based inference for the parameters in a generalized partially linear single-index models (GPLSIM) is investigated. Based on the local linear estimators of the nonparametric parts of the GPLSIM, an estimated empirical likelihood-based statistic of the parametric components is proposed. We show that the resulting statistic is asymptotically standard chi-squared distributed, the confidence regions for the parametric components are constructed. Some simulations are conducted to illustrate the proposed method.     

Empirical Likelihood Inferences for Semiparametric Varying-Coefficient Partially Linear Models with Longitudinal Data

In this article, empirical likelihood inferences for semiparametric varying-coefficient partially linear models with longitudinal data are investigated. We propose a groupwise empirical likelihood procedure to handle the inter-series dependence of the longitudinal data. By using residual-adjustment, an empirical likelihood ratio function for the nonparametric component is constructed, and a nonparametric version Wilks' phenomenons is proved. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. A simulation study is undertaken to assess the finite sample performance of the proposed confidence regions.     

Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random

Abstract.  A kernel regression imputation method for missing response data is developed. A class of bias-corrected empirical log-likelihood ratios for the response mean is defined. It is shown that any member of our class of ratios is asymptotically chi-squared, and the corresponding empirical likelihood confidence interval for the response mean is constructed. Our ratios share some of the desired features of the existing methods: they are self-scale invariant and no plug-in estimators for the adjustment factor and asymptotic variance are needed; when estimating the non-parametric function in the model, undersmoothing to ensure root- n consistency of the estimator for the parameter is avoided. Since the range of bandwidths contains the optimal bandwidth for estimating the regression function, the existing data-driven algorithm is valid for selecting an optimal bandwidth. We also study the normal approximation-based method. A simulation study is undertaken to compare the empirical likelihood with the normal approximation method in terms of coverage accuracies and average lengths of confidence intervals.     

Empirical Likelihood-Based Inferences for Generalized Partially Linear Models

Abstract.  This paper considers generalized partially linear models. We propose empirical likelihood-based statistics to construct confidence regions for the parametric and non-parametric components. The resulting statistics are shown to be asymptotically chi-square distributed. Finite-sample performance of the proposed statistics is assessed by simulation experiments. The proposed methods are applied to a data set from an AIDS clinical trial.     

Empirical Likelihood Inference for Longitudinal Data with Missing Response Variables and Error-Prone Covariates

We consider statistical inference for longitudinal partially linear models when the response variable is sometimes missing with missingness probability depending on the covariate that is measured with error. The block empirical likelihood procedure is used to estimate the regression coefficients and residual adjusted block empirical likelihood is employed for the baseline function. This leads us to prove a nonparametric version of Wilk's theorem. Compared with methods based on normal approximations, our proposed method does not require a consistent estimators for the asymptotic variance and bias. An application to a longitudinal study is used to illustrate the procedure developed here. A simulation study is also reported.