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1.
增长曲线模型回归系数线性估计的泛容许性 总被引:7,自引:0,他引:7
本文讨论增长曲线模型回归系数的线性估计的容许性.我们给出了回归系数线性估计的泛容许性定义,并在某些线性估计类中得到了泛容许估计的充要条件. 相似文献
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多元线性模型中随机回归系数和参数的线性估计的泛容许性 总被引:7,自引:0,他引:7
本文对于一般的随机效应多元线性模型,给出了随机回归系数和参数的线性可估函数的泛容许性估计的定义,并得到了随机回归系数和参数的线性可估函数的齐线性估计在齐线性估计类中泛容许性的特征。 相似文献
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在矩阵损失函数下,讨论了一般增长曲线模型中回归系数线性估计的可容许性问题,分别在齐次与非齐次估计类中给出了回归系数的线性估计是可容许估计的充要条件,推广了以往文献的相关结论. 相似文献
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该文讨论了增长曲线模型$Y=X_{1}BX_{2}+\epsilon$在约束条件$X_{2}'B'X_{1}'NX_{1}BX_{2}\leq\Sigma$下回归系数线性估计$DYF$的泛可容许性问题,在损失函数$(d(Y)-KBL)'(d(Y)-KBL)$下,给出了回归系数的线性估计是泛可容许性的充要条件,其结果推广了文献中已有的结论. 相似文献
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对回归系数在不等式约束和平衡损失下讨论了其线性估计的可容许性,给出了齐次和非齐次线性估计类中可容许估计的充要条件. 相似文献
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在二次矩阵损失函数下研究了协方差矩阵未知的多元线性模型中回归系数矩阵的可估线性函数的矩阵非齐次线性估计的可容许性,给出了矩阵非齐次线性估计在线性估计类中可容许的一个充要条件. 相似文献
10.
矩阵损失下生长曲线模型中回归系数线性函数的MINIMAX可容许估计 总被引:3,自引:0,他引:3
本文在矩阵损失下给出了生长曲线模型中回归系数线性估计在某种线性估计类中是Minimax可容许估计的充要条件 相似文献
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Weak and universal consistency of moving weighted averages 总被引:1,自引:0,他引:1
H. -G. Müller 《Periodica Mathematica Hungarica》1987,18(3):241-250
The properties of weighted averages as linear estimators of a regression function and its derivatives are investigated for the fixed design case. Results on weak consistency and on universal consistency are derived, using a modification of the definition of Stone [10]. As examples we consider kernel estimates and weighted local regression estimators and show that the general results apply. 相似文献
12.
Lubomír Kubáček 《Mathematica Slovaca》2010,60(3):411-418
In the universal linear statistical model with the type II constraints, estimates of the unbiasedly estimable linear functions
of the parameters of the mean value vector are given by special types of generalized matrix inverse. Since there exists many
versions of such matrix inverse it is of some interest to check the unambiguity of obtained estimators. The aim of the paper
is to find the best unbiased linear estimators of unbiasedly estimable functions and to show that they do not depend on the
choice of the used generalized inverse of the matrices. 相似文献
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AClassofLinearBiasedEstimatorsofRegressionParameterMatrixintheGrowthCurveModel¥GuiQingming(ZhengzhouInstituteofSurveyingandMa... 相似文献
14.
Jose M. Vidal-Sanz Miguel A. Delgado 《Annals of the Institute of Statistical Mathematics》2004,56(4):791-818
This paper considers delta estimators of the Radon-Nikodym derivative of a probability function with respect to a σ-finite
measure. We provide sufficient conditions for universal consistency, which are checked for some wide classes of nonparametric
estimators. 相似文献
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Global optimization problems are often approached by branch and bound algorithms which use linear relaxations of the nonlinear constraints computed from the current variable bounds. This paper studies how to derive safe linear relaxations to account for numerical errors arising when computing the linear coefficients. It first proposes two classes of safe linear estimators for univariate functions. Class-1 estimators generalize previously suggested estimators from quadratic to arbitrary functions, while class-2 estimators are novel. When they apply, class-2 estimators are shown to be tighter theoretically (in a certain sense) and almost always tighter numerically. The paper then generalizes these results to multivariate functions. It shows how to derive estimators for multivariate functions by combining univariate estimators derived for each variable independently. Moreover, the combination of tight class-1 safe univariate estimators is shown to be a tight class-1 safe multivariate estimator. Finally, multivariate class-2 estimators are shown to be theoretically tighter (in a certain sense) than multivariate class-1 estimators. 相似文献
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Admissibility of linear estimators of a regression coefficient in linear models with and without the assumption that the underlying distribution is normal is discussed under a balanced loss function. In the non-normal case, a necessary and sufficient condition is given for linear estimators to be admissible in the space of homogeneous linear estimators. In the normal case, a sufficient condition is provided for restricted linear estimators to be admissible in the space of all estimators having finite risks under the balanced loss function. Furthermore, the sufficient condition is proved to be necessary in the normal case if additional conditions are assumed. 相似文献
17.
Jianqing Fan Theo Gasser Irène Gijbels Michael Brockmann Joachim Engel 《Annals of the Institute of Statistical Mathematics》1997,49(1):79-99
We consider local polynomial fitting for estimating a regression function and its derivatives nonparametrically. This method possesses many nice features, among which automatic adaptation to the boundary and adaptation to various designs. A first contribution of this paper is the derivation of an optimal kernel for local polynomial regression, revealing that there is a universal optimal weighting scheme. Fan (1993, Ann. Statist., 21, 196-216) showed that the univariate local linear regression estimator is the best linear smoother, meaning that it attains the asymptotic linear minimax risk. Moreover, this smoother has high minimax risk. We show that this property also holds for the multivariate local linear regression estimator. In the univariate case we investigate minimax efficiency of local polynomial regression estimators, and find that the asymptotic minimax efficiency for commonly-used orders of fit is 100% among the class of all linear smoothers. Further, we quantify the loss in efficiency when going beyond this class. 相似文献
18.
Admissibility of linear estimators with respect to inequality constraints under matrix loss function
In this paper we investigate the admissibility of linear estimators in the multivariate linear model with respect to inequality constraints under matrix loss function. The necessary and sufficient conditions for a linear estimator to be admissible in the class of homogeneous linear estimators and the class of inhomogeneous linear estimators are obtained, respectively. 相似文献
19.
P. N. Sapozhnikov 《Journal of Mathematical Sciences》1997,84(3):1151-1161
A new technique of optimal estimation of density functions for exponential shift families on a homogeneous space of a Lie
group is proposed. In contrast to traditional methods, the approach considered is essentially based on the algebraic properties
of shift families. Here we give a universal formula for consistent estimators of density functions covering different classes
of estimators such as unbiased estimators with uniformly minimum variance and Bayesian estimators under two popular loss functions.
The representations of some maximal invariant density functions are derived and simultaneously a close connection between
the estimators and these density functions is established.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III. 相似文献
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不等式约束下线性模型中线性估计的可容许性 总被引:6,自引:0,他引:6
研究了线性模型在不等式约束条件下齐次和非齐次线性估计的可容许性,刻画了两者之间的关系,得到了不等式约束条件下非齐次线性估计可容许性的充要条件. 相似文献