线性模型参数的稳健化有偏估计

本文讨论复共线性和粗差同时存在时线性模型的参数估计问题,基于等价权原理提出了一个稳健有偏估计类（稳健压缩估计）,并且建立了稳健压缩估计的计算方法,为了满足实际问题的需要,构造了许多很有意义的稳健有偏估计,例如稳健岭估计、稳健主成分估计,稳健组合主成估计、稳健单参数主成分估计、稳健根方估计等等,最后通过一个算例表明,本文提出的稳健有偏估计具有既可克服复共线性影响又可抵抗粗差干扰的良好性质。     

部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.     

线性回归模型参数的泛BC估计

本在献[1]的基础上，提出了线性回归模型参数的泛BC估计，把有偏压缩估计类的压缩系数由一维推广到多维，即由常数推广到矩阵向量，从而推出其一些优良性质。     

部分线性变系数模型改进的加权混合Profile-Liu估计

研究半参数部分线性变系数模型的有偏估计,当回归模型参数部分自变量存在多重共线性时,在随机线性约束条件下,融合Profile最小二乘估计、加权混合估计和Liu估计构造回归模型参数分量改进的加权混合Profile-Liu估计,并在一定正则条件下证明估计量的渐近性质,最后利用蒙特卡洛数值模拟验证所提出估计量的有限样本表现性.     

多元线性模型回归系数的有偏估计与均方误差的无偏估计

本文对多元线性模型回归系数的最小二乘估计的任一线性变换，给出了均方误差的一个无偏估计，并应用统一方法，即极小化均方误差的无偏估计的方法，对岭估计和广义岭估计给出了确定偏参数的公式。最后给出了一个实例。     

混合系数线性模型的几乎无偏岭估计

本文研究了连续测量数据情况下的混合系数线性模型的参数估计问题.利用岭估计方法得到了该模型的几乎无偏岭估计,并证明了在均方误差意义下,几乎无偏岭估计优于岭估计.最后讨论了有偏参数的选取问题.     

混合系数线性模型参数的广义Liu估计

本文研究连续测量数据情况下的混合系数线性模型的参数估计问题.利用压缩估计方法给出了该模型的一类新的有偏估计-广义Liu估计,并在均方误差意义下,证明此类估计分别优于最小二乘估计、Liu估计.最后讨论参数的选取问题.     

带约束线性模型中的可容许线性估计

带约束线性模型中的可容许线性估计张双林（黑龙江大学数学系，哈尔滨１５００８０）１．引言及主要结果考虑线性模型当参数不受约束时，Ｒａｏ［１］，吴启光［２］，朱显海和鹿长余［３］等给出了Ｓｎ×Ｐβ的线性估计在线性类中是可容许的充要条件，当参数在约束条件，...     

线性等式约束下奇异线性模型参数的条件BLU估计

考虑带线性等式约束的奇异线性模型对任一条伯可估函数Ｃ’β，本文给出了它的所有条件ＢＬＵ估计，并建立了Ｃ‘（Ｘ’Ｘ）＋Ｘ‘ｙ为Ｃ’β的条件ＢＬＵ估计的一个充分条件。最后研究了带线性等式约束的多元线性模型参数阵的条件ＢＬＵ估计。     

二项分布参数n的线性可容许估计（英）

本文考虑了二项分布B（ｎ，ｐ）当ｐ已知时整值参数ｎ的估计问题，并且得到了一个ｎ的线性估计为可容许估计的充分必要条件．     

A Class of Linear Biased Estimators of Regression ParameterMatrix in the Growth Curve Model

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Adaptive Unified Biased Estimators of Parameters in Linear Model

To tackle multi collinearity or ill-conditioned design matrices in linear models,adaptive biasedestimators such as the time-honored Stein estimator,the ridge and the principal component estimators havebeen studied intensively.To study when a biased estimator uniformly outperforms the least squares estimator,some sufficient conditions are proposed in the literature.In this paper,we propose a unified framework toformulate a class of adaptive biased estimators.This class includes all existing biased estimators and some newones.A sufficient condition for outperforming the least squares estimator is proposed.In terms of selectingparameters in the condition,we can obtain all double-type conditions in the literature.     

回归系数的广义根方估计及其模拟

文献[1,2]中提出了回归系数的根方估计~(k),当回归自变量间存在复共线关系时,~(k)较回归系数的最小二乘估计有所改善,本文将根方估计作一拓广,得出了回归系数的广义根方估计~(K),其中K为对角阵,文中证明了广义根方估计~(K)较~(k)能更有效地改善最小二乘估计,并给出了广义根方估计的显式解,在此基础上,提出了广义根方估计的显式解和一种确定k_i的方法。     

A Class of Biased Estimators Besed on SVD in Linear Model

In this paper,a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill-conditioning in the design matrix.Some important properties of these new estimators are obtained.By appropriate choices of the biased parameters,we construct many useful and important estimators.An application of these new estimators in three-dimensional position adjustment by distance in a spatial coordiate surveys is given.The results show that the proposed biased estimators can effectively overcome ill-conditioning and their numerical stabilities are preferable to ordinary least square estimation.     

线性模型中基于SVD的一个新的有偏估计类

§1 .　IntroductionTheproblemofill_conditioninganditsstatisticalconsequencesonalinearregressionmodelarewell_knowninstatistics(Vinod&Ullah 1981;Belsley 1991) .Itis,forinstance ,knownthatoneofthemajorconsequencesofill_conditioningontheleastsquares(LS)regressionesti matoristhattheestimatorproduceslargesamplingvariance,whichinturnmightinappropri atelyleadtoexclusionofotherwisesignificantcoefficientfromthemodel,andthesignsofcoef ficientscanbecontrarytointuitionetc..Tocircumventthisproblem ,manybi…     

非零截距线性和非线性回归模型的T-型稳健估计算法

首先给出非零截距线性模型T-型估计的模型与EM算法,其次给出非线性回归模型参数的T-型估计,利用泰勒级数对模型线性化,得到参数估计的迭代算法,最后用数值模拟实验验证了该算法的正确性和证实了T-型估计的稳健性.     

Generalized Partially Linear Measurement Error Models

This article considers generalized partially linear models when the linear covariate is measured with additive error. We propose estimators of parameter and nonparametric function by using local linear regression, the SIMEX technique, and generalized estimating equation. The asymptotic normality of the estimators of the parameter, and bias and variance of the estimators of the nonparametric component are derived under appropriate assumptions. In addition, the generalization to clustered measurements is discussed. The approaches are used to the analysis of data from the Framingham Heart Study. A simulation experiment is conducted for an illustration.     

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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We propose a new estimation method for the parameters of a partial functional linear model when the parameter curve is subject to monotone constraint. The proposed estimators are implemented under the nonlinear mixed effects model framework. The small sample properties are illustrated through a simulation experiment.