误差为NSD序列的广义线性模型的M估计的强相合性

研究了以NSD序列(negatively superadditive dependent)为误差的广义线性模型,得到了未知参数的M估计.在较弱的条件下,利用指数不等式、NSD序列加权和的强收敛性和Borel-Cantelli引理等证明了未知参数M估计的强相合性.此结果推广了独立误差和NSD误差的线性模型的相应结果.     

具有相关误差的多元线性模型的更新方程

已知的线性模型的更新方程是在对模型加了不相关误差结构的约束, 或只对带有固定参数的一元线性模型考虑的. 本文考虑具有相关误差的多元线性模型下的更新方程, 给出了在补充参数, 数据或指标时, 未知参数阵的最佳线性无偏估计及残积阵的更新方程. 公式适用于固定参数与随机参数两种情形.     

一般线性混合模型中的最佳线性无偏估计和谱分解估计

该文在一般线性混合模型中, 研究了固定和随机效应线性组合的估计问题.对观测向量的协方差阵可以为奇异矩阵情形下,导出了该组合的最佳线性无偏估计,并证明了它的唯一性.在一般线性混合模型的特例, 三个小域模型下, 得到了小域均值u_i 和方差分量的谱分解估计. 进而, 获得了基于谱分解估计的两步估计均方误差的二阶逼近.     

相依线性回归模型M-估计的线性表示（英文）

本文考虑如下线性回归模型y_i=x_i~Tβ+e_i,i=1,2…,n,其中e_i=G(…,ε_(i-1),ε_i)是平稳相依误差,ε_i,i∈Z是独立同分布的随机变量.在非凸函数的情形下,得到了参数β的M-估计的线性表示,并由此得到两个应用:强收敛速度和正态分布.最后,用一模拟算例来说明本文方法的有效性.     

Banach空间中闭线性算子广义预解式存在定理

在Banach空间中研究闭线性算子广义逆扰动问题和广义预解式存在性问题.给出了闭线性算子广义逆在T-有界扰动下的一些稳定特征,这些特征推广了在有界线性算子情形、闭线性算子有界扰动情形以及闭线性算子保值域或保核空间情形的一些已知结果.以此为基础,得到了闭线性算子广义预解式存在的一些充要条件及其广义预解式的显式表达式.作为应用,给出了闭Fredholm算子和闭半-Fredholm算子的广义预解式存在性特征.     

线性模型中误差为相依情形下误差方差估计的Berry—Esseen界限

本文主要讨论了线性模型中误差为α－混合强一稳序列情形下，误差方差估计的Ｂｅｒｒｙ－Ｅｓｓｅｅｎ界限，其阶为ｎ＾－１／２＋λ。     

一类临界拟线性椭圆型方程组解的存在性

本文讨论了一类临界拟线性椭圆型方程组解的存在性问题.利用LionsPL提出的第二集中紧性原理和山路引理,证明了该方程组在超线性扰动情形下非平凡解的存在性.此外,利用极值原理,也得到了该方程组在次线性扰动情形存在非平凡解.     

鞅差误差下线性EV模型最小二乘估计的中偏差

研究了线性EV模型:η_i=θ+βx_i+ε_i,ξ_i=x_i+δ_i,1≤i≤n.当误差(ε_i,δ_i)为鞅差序列情形时,讨论了未知参数β和θ的最小二乘估计的中偏差问题.     

拓扑线性空间中的Drop定理

本文在拓扑线性空间中建立了一般的Drop定理并证明新的Drop定理与拓扑线性空间中的一个Ekeland变分原理型的结果等价.此外,还给出了一个无界Drop情形下的Drop定理.     

n阶变系数线性微分方程组的可解情形

本文讨论了 n阶变系数线性微分方程在变量代换下可化为可解方程组的问题 ,把文 [1 ]的二阶情形推广至 n阶情形 ,且例举了三阶情形 .     

Linear plus quadratic (LPQ) quasiminimax estimation in the linear regression model

If the errors in the linear regression model are assumed to be independent with nonvanishing third and finite fourth moments, then it is possible to improve all linear estimators by so-called linear plus quadratic (LPQ) estimators. These consist of linear and quadratic terms in the endogeneous variable and depend on the unknown moments of the errors which, in general, have to be estimated from the data. In this paper, we will use LPQ estimators for quasiminimax estimation and some related problems.Support by Deutsche Forschungsgemeinschaft Grant No. Tr 253/1-2 is gratefully acknowledged.     

Minimum Disparity Estimation in Linear Regression Models: Distribution and Efficiency

This paper deals with the minimum disparity estimation in linear regression models. The estimators are defined as statistical quantities which minimize the blended weight Hellinger distance between a weighted kernel density estimator of errors and a smoothed model density of errors. It is shown that the estimators of the regression parameters are asymptotic normally distributed and efficient at the model if the weights of the density estimators are appropriately chosen.     

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In this paper, we consider the estimation problem for partially linear models with additive measurement errors in the nonparametric part. Two kinds of estimators are proposed. The first one is an integral moment-based estimator with deconvolution kernel techniques, associated with the strong consistency for the estimator. Another one is a simulation-based estimator to avoid the integrals involved in the integral moment-based estimator. Simulation studies are conducted to examine the performance of the proposed estimators.     

因变量缺失下线性变量含误差模型的估计

主要考虑线性模型在自变量测量含误差以及因变量缺失情况下的估计问题.对于模型中的回归系数,我们基于最小二乘方法提出了两类估计,其中一类估计只由完整观测数据构成,而另外一类估计利用的则是利用简单插补方法构造的完整数据.证明了这两类估计是渐近正态性的.     

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Using wavelet smoothing and least-squares methods,we investigate a heteroscedastic partly linear errors-in-variables (EV)model with $\alpha$-mixing random errors. The wavelet estimators of the parametric parts and nonparametric parts are given, and Berry-Esseen bounds of wavelet estimators are obtained under general conditions.     

因变量缺失下部分线性变系数变量含误差模型的估计

该文主要考虑部分线性变系数模型在自变量含有测量误差以及因变量存在缺失情形下的估计问题.基于Profile最小二乘技术,针对参数分量和非参数分量提出了多种估计方法.第一种估计方法只利用了完整观测数据,而第二种和第三种估计方法分别利用了插补技术和替代技术.参数分量的所有估计被证明是渐近正态的,非参数分量的所有估计被证明和一般非参数回归函数的估计具有相同的收敛速度.对于因变量的均值,构造了两类估计并证明了它们的渐近正态性.最后,通过数值模拟验证了所提方法.     

一类线性回归模型中核估计的渐近性质

考虑固定设计下具有一阶非参数自回归误差的线性模型,构造了参数和非参数函数的N-W核估计,在适当的条件下,证明了参数估计的强相合性,同时给出了非参数函数估计的渐近正态性.     

Limiting Distributions of Linear Programming Estimators

Smith (1994) proposes estimation in linear regression models with non-negative errors by maximizing the sum of fitted values subject to the constraint that the fitted values can be no larger than the corresponding response value. In this paper, we consider the limiting distribution of these estimators under very general conditions. Some extensions to local polynomial estimation are also considered.     

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??In this paper, semiparametric estimation of a regression function in the third order partially linear autoregressive model with first order autoregressive errors is mainly studied. We suppose that the regression function has a parametric framework, and use the conditional least squares method to obtain the parameter estimators. Then semiparametric estimators of the regression function can be given by combining with the nonparametric kernel function adjustment. Furthermore, under certain conditions, the consistency of the estimators is proved. Finally, simulation research is presented to evaluate the effectiveness of the proposed method.     

Efficient Mean Estimation in Log-Normal Linear Models with First-Order Correlated Errors

In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error (MM) and the asymptotic bias (MB), respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.