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本文研究了平衡损失函数下正态总体和非正态总体中有限回归系数的可容许预测.利用统计决策理论,获得了非正态总体中齐次线性预测为可容许预测的充分必要条件和在正态总体中齐次线性预测在一切预测类中可容许性的充要条件,推广了二次损失下的若干相关结果. 相似文献
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本文研究了带有不等式约束的多指标线性模型中线性估计的可容许性.利用矩阵论的相关知识,在矩阵损失下得到了齐次线性估计在齐次线性估计类中是可容许的充要条件,以及非齐次线性估计在非齐次线性估计类中是可容许的若干条件,推广了不等式约束下可容许性的相关结果. 相似文献
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《数学物理学报(A辑)》2010,(6)
该文研究了协方差矩阵未知的多元线性模型中,二次矩阵损失函数下回归系数矩阵可估线性函数的非齐次线性估计的可容许性.不需正态分布的假设,作者给出矩阵非齐次线性估计在线性估计类中可容许的充要条件;在正态分布的假设下,作者给出矩阵非齐次线性估计在一切估计组成的估计类中可容许的充分条件. 相似文献
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本文讨论了向量损失函数下参数估计的可容许与在常用损失函数下可容许之间的关系 ,并研究了在一元线性模型、多元线性模型中参数估计在特定估计类及一切估计类中的可容许性 ,给出了估计可容许的一些充要条件和充分条件 . 相似文献
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对一般线性模型在平方损失函数下,得到了一维不可估参数函数的线性估计为可容许估计的充要条件,以及模型中参数向量(非线性可估)的线性估计为可容许估计的两个充要条件,并得到了多维参数函数(可估或不可估)的线性估计为可容许估计的一个充分条件以及特殊情况下的一个充要条件. 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
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Guo Hua Zou 《数学学报(英文版)》2002,18(1):37-46
This paper considers the admissibility of the estimators for finite population when the parameter space is restricted. We
obtain all admissible linear estimators of an arbitrary linear function of characteristic values of a finite population in
the class of linear estimators under the criterion of the expectation of mean squared error.
Received February 12, 1999, Revised October 8, 1999, Accepted January 14, 2000 相似文献
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Admissible estimation of linear functions of characteristic values of a finite population 总被引:1,自引:0,他引:1
The problem on admissibility of estimators is considered based on the point of view of the superpopulation model. The necessary
and sufficient conditions for linear estimators of an arbitrary linear function of characteristic values of a finite population
to be admissible in the class of linear or all estimators are obtained respectively.
Project supported by the National Natural Science Foundation of China. 相似文献
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A note on ratio and product type estimators 总被引:1,自引:0,他引:1
S. K. Ray Ashok Sahai Ajit Sahai 《Annals of the Institute of Statistical Mathematics》1979,31(1):141-144
Summary The use of ratio and product estimators for the mean of a finite population is well known. This paper proposes transformed
estimators obtained through parametric linear combination of the ratio, or product, and the usual unbiased estimator of the
mean for any sample design. To the first degree of approximation, the proposed estimators have smaller mean square error than
that of the ratio, product and the usual unbiased estimator, for suitable choice of the parameter. The superiority of the
proposed estimators over others for small samples has been studied empirically. 相似文献
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Zhang Gangqiang 《大学数学》1998,(2)
本文在EV(Eror in Variables)超总体模型下讨论有限总体两个指标值的同时估计问题,证明了样本均值作为整体均值的估计在均方差阵最小的意义下是最优的. 相似文献
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利用分层抽样数据中完全辅助信息的模型校正方法 总被引:1,自引:0,他引:1
In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG). 相似文献
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Dankmar Böhning Uwe Malzahn Jesus Sarol Jr Sasivimol Rattanasiri Annibale Biggeri 《Annals of the Institute of Statistical Mathematics》2002,54(4):827-839
In this paper the situation of extra population heterogeneity in the standardized mortality ratio is discussed from the point-of-view of an analysis of variance. First, some simple non-iterative ways are provided to estimate the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself. Next, a wider class of linear unbiased estimators is introduced and their properties investigated. Consistency is shown for a wide sub-class of estimators charactererized by the fact that the associated linear weights are within some positive, finite bounds. Furthermore, it is shown that an efficient estimator is often provided when the weights are proportional to the expected counts. 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
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M. D. Martínez-Miranda M. Rueda-Garcia A. Arcos-Cebrián Y. Román-Montoya S. Gonzalez-Aguilera 《Computational Statistics》2005,20(3):385-399
This paper deals with the estimation, under sampling in two successive occasions, of a finite population quantile. For this
sampling design a class of estimators is proposed whose the ratio and difference estimators are particular cases. Asymptotic
variance formulae are derived for the proposed estimators, and the optimal matching fraction is discussed. Comparisons are
made with existing estimators in a simulation study using a natural population. 相似文献
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对于2SUR回归模型的参数估计问题,给出了一些一航均方误差矩阵比较结果,据此提出了一类线性估计和一类基于离差阵广义非限定估计的非线性两步估计,并获得了该两步估计类的一些有限样本性质。 相似文献
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本文提出两个新的估计量,利用观察数据中的总体辅助信息来估计有限总体分布函数,并通过两个人工总体的模拟实验,比较新的估计量、传统的估计量及Rao,Kover&Mantel(1990)提出的估计量的相对平均误差与相对标准差。结果表明,从相对标准差的角度分析,两个新的估计量有一个是四个估计量中精度最好的一个,另一个也有很好的表现;而且它们在模型有所偏差时都具备了较好的稳健性。 相似文献