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考虑了误差为NA序列的半参数回归模型,利用非参数估计方法给出了模型参数的最小二乘估计和加权最小二乘估计,并在适当条件下得到了它们的矩相合性. 相似文献
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线性模型中φ混合误差下回归系数最小二乘估计的相合性 总被引:1,自引:0,他引:1
杨善朝 《数理统计与应用概率》1994,9(1):84-91
本文研究线性模型中φ-混合误差序列下回归系数最小二乘估计的相合性,分别对最小二乘估计为强相合和r阶平均相合给出一些充分条件。 相似文献
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当自变量间存在复共线性时,最小二乘估计就表现出不稳定并可能导致错误的结果。本采用广义岭估计β(K)来估计多元线性模型的回归系数β=vec(B),通过岭参数K值的选取 ,可使广义岭估计的均方误差MSE小于最小二乘估计的MSE。指出了广义岭估计中根据MSE准则选取K值存在的主要缺陷,采用了一种选取K值的新准则Q(c),它包含MSE准则和最小二乘LS准则作为特例,从理论上证明和讨论了Q(c)准则的优良性,阐明了c值的统计 含义,并给出了确定c值的方法。 相似文献
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以离散小波变换为工具,利用其特有的低通滤波属性和有效的抑制测量噪声的能力,将其与传统的最小二乘估计相结合,建立了一种基于小波测量预处理的改进最小二乘估计新方法,获得了比传统最小二乘估计好得多的估计结果;计算机仿真验证了算法的有效性. 相似文献
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当自变量间存在复共线性时,最小二乘估计就表现出不稳定并可能导致错误的结果.本文采用广义岭估计β(K)来估计多元线性模型的回归系数β=vec(B),通过岭参数K值的选取,可使广义岭估计的均方误差MSE小于最小二乘估计的MSE.指出了广义岭估计中根据MSE准则选取K值存在的主要缺陷,采用了一种选取K值的新准则Q(c),它包含MSE准则和最小二乘LS准则作为特例,从理论上证明和讨论了Q(c)准则的优良性,阐明了c值的统计含义,并给出了确定c值的方法. 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):209-223
This paper is devoted to the problem of minimax estimation of parameters in linear regression models with uncertain second order statistics. The solution to the problem is shown to be the least squares estimator corresponding to the least favourable matrix of the second moments. This allows us to construct a new algorithm for minimax estimation closely connected with the least squares method. As an example, we consider the problem of polynomial regression introduced by A. N. Kolmogorov 相似文献
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We consider the problem of estimating regression models of two-dimensional random fields. Asymptotic properties of the least squares estimator of the linear regression coefficients are studied for the case where the disturbance is a homogeneous random field with an absolutely continuous spectral distribution and a positive and piecewise continuous spectral density. We obtain necessary and sufficient conditions on the regression sequences such that a linear estimator of the regression coefficients is asymptotically unbiased and mean square consistent. For such regression sequences the asymptotic covariance matrix of the linear least squares estimator of the regression coefficients is derived. 相似文献
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In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal.An iterative weighted partial spline least squares estimator(IWPSLSE)for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE)with weights constructed by using the within-group partial spline least squares residuals in the sense 相似文献
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Yan-meng Zhao Jin-hong You Yong Zhou 《应用数学学报(英文版)》2006,22(4):565-574
A partially linear regression model with heteroscedastic and/or serially correlated errors is studied here. It is well known that in order to apply the semiparametric least squares estimation (SLSE) to make statistical inference a consistent estimator of the asymptotic covariance matrix is needed. The traditional residual-based estimator of the asymptotic covariance matrix is not consistent when the errors are heteroscedastic and/or serially correlated. In this paper we propose a new estimator by truncating, which is an extension of the procedure in White. This estimator is shown to be consistent when the truncating parameter converges to infinity with some rate. 相似文献
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基于共轭梯度法的思想,通过特殊的变形,建立了一类求矩阵方程AXA^T+BYB^T=C的双对称最小二乘解的迭代算法.对任意的初始双对称矩阵.在没有舍人误差的情况下,经过有限步迭代得到它的双对称最小二乘解;在选取特殊的初始双对称矩阵时,能得到它的的极小范数双对称最小二乘解.另外,给定任意矩阵,利用此方法可得到它的最佳逼近双对称解,数值例子表明,这种方法是有效的. 相似文献
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The ordinary least squares estimation is based on minimization of the squared distance of the response variable to its conditional
mean given the predictor variable. We extend this method by including in the criterion function the distance of the squared
response variable to its second conditional moment. It is shown that this “second-order” least squares estimator is asymptotically
more efficient than the ordinary least squares estimator if the third moment of the random error is nonzero, and both estimators
have the same asymptotic covariance matrix if the error distribution is symmetric. Simulation studies show that the variance
reduction of the new estimator can be as high as 50% for sample sizes lower than 100. As a by-product, the joint asymptotic
covariance matrix of the ordinary least squares estimators for the regression parameter and for the random error variance
is also derived, which is only available in the literature for very special cases, e.g. that random error has a normal distribution.
The results apply to both linear and nonlinear regression models, where the random error distributions are not necessarily
known. 相似文献
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Asymptotic distribution of the weighted least squares estimator 总被引:3,自引:0,他引:3
Jun Shao 《Annals of the Institute of Statistical Mathematics》1989,41(2):365-382
This paper derives the asymptotic distribution of the weighted least squares estimator (WLSE) in a heteroscedastic linear regression model. A consistent estimator of the asymptotic covariance matrix of the WLSE is also obtained. The results are obtained under weak conditions on the design matrix and some moment conditions on the error distributions. It is shown that most of the error distributions encountered in practice satisfy these moment conditions. Some examples of the asymptotic covariance matrices are also given. 相似文献
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利用Pena距离对加权线性最小二乘估计的影响问题进行讨论,得到加权最小二乘估计的Pena距离的表达式,对其性质进行讨论,从而得到高杠异常点的判别方法.文中对Pena距离与Cook距离的性能进行了对比,得到在一定条件下Pena距离优于Cook距离的结论.并通过数值实验对此方法的有效性进行验证. 相似文献