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本文提出用经验似然重抽样来bootstrap逼近线性回归模型中的学生化最小二乘估计.我们证明了该方法具有一般s-2项Edgeworth展开,它是二阶相合的而且比经典的方法损失更小. 相似文献
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用线性贝叶斯方法去同时估计线性模型中回归系数和误差方差,并在不知道先验分布具体形式的情况下,得到了线性贝叶斯估计的表达式.在均方误差矩阵准则下,证明了其优于最小二乘估计和极大似然估计.与利用MCMC算法得到的贝叶斯估计相比,线性贝叶斯估计具有显式表达式并且更方便使用.对于几种不同的先验分布,数值模拟结果表明线性贝叶斯估... 相似文献
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本文应用经验似然方法得到了线性模型误差方差的一类新的估计,证明了估计的渐近分布为正态分布且渐近方差不超过常用的误差方差估计的渐近方差,同时给出了渐近方差的显式表达. 相似文献
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极大似然估计作为参数估计中较为有效的一种估计方法,在误差分布未知下无法进行,另一方面,时空数据经常含有奇异点或来自重尾分布,此时基于最小二乘的估计方法效果欠佳.考虑时空异质性和相关性,针对误差分布未知的时空模型,本文提出基于核密度估计的自适应非参数估计方法.在较弱的条件下证明了该估计量和已知误差分布下的局部极大似然估计... 相似文献
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《数学的实践与认识》2020,(4)
在随机缺失(MAR)机制下利用经验似然方法构造了线性回归模型中误差方差的估计.并在一定条件下,证明了该估计的渐近正态性,由此得出当误差的分布不对称时,该估计的渐近方差比常用估计的渐近方差小. 相似文献
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高维线性回归估计是一个被大量学者研究的重要统计学问题.在误差分布未知的情况下,如何将有效性纳入高维估计仍是一个尚未解决且具有挑战性的问题.最小二乘估计在非Gauss误差密度下会损失估计的效率,而极大似然估计由于误差密度未知,无法直接被应用.基于惩罚估计方程,本文提出一种新的稀疏半参有效估计方法应用于高维线性回归的估计.本文证明了在误差密度未知的超高维回归下,新的估计渐近地与具有神谕性的极大似然估计一样有效,因此对于非Gauss误差密度,它比传统的惩罚最小二乘估计更有效.此外,本文证明了几种常用的高维回归估计是本文方法的特例.模拟和实际数据的结果验证了本文所提出方法的有效性. 相似文献
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研究了一个简化的新的Laplace AR(1)模型参数的条件最小二乘估计和最大拟似然估计,并讨论了它们的强相合性和渐近正态性.通过数值模拟和实际例子,说明了最大拟似然估计及模型的优越性. 相似文献
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分析了基于Jeffreys验前的经典Bayes方差估计以及考虑验前信息可信度情况下Bayes方差估计存在的问题,在一般情况下,其方差估计要大于验前子样和验后子样的方差,这显然是不合理的.这是采用Jeffreys验前和正态共轭分布假设时存在的固有问题.为了解决这一问题,提出了方差估计的修正公式,经过计算验证,其值在验前子样和验后子样方差之间,说明修正公式是合理的. 相似文献
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In this article, we consider sufficient dimension folding for the regression mean function when predictors are matrix- or array-valued. We propose a new concept named central mean dimension folding subspace and its two local estimation methods: folded outer product of gradients estimation (folded-OPG) and folded minimum average variance estimation (folded-MAVE). We establish the asymptotic properties for folded-MAVE. A modified BIC criterion is used to determine the dimensions of the central mean dimension folding subspace. We evaluate the performances of the two local estimation methods by simulated examples and demonstrate the efficacy of folded-MAVE in finite samples. And in particular, we apply our methods to analyze a longitudinal study of primary biliary cirrhosis. Supplementary materials for this article are available online. 相似文献
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The paper is dealing with estimation of rare event probabilities in stochastic networks. The well known variance reduction
technique, called Importance Sampling (IS) is an effective tool for doing this. The main idea of IS is to simulate the random
system under a modified set of parameters, so as to make the occurrence of the rare event more likely. The major problem of
the IS technique is that the optimal modified parameters, called reference parameters to be used in IS are usually very difficult
to obtain. Rubinstein (Eur J Oper Res 99:89–112, 1997) developed the Cross Entropy (CE) method for the solution of this problem
of IS technique and then he and his collaborators applied this for estimation of rare event probabilities in stochastic networks
with exponential distribution [see De Boer et al. (Ann Oper Res 134:19–67, 2005)]. In this paper, we test this simulation
technique also for medium sized stochastic networks and compare its effectiveness to the simple crude Monte Carlo (CMC) simulation.
The effectiveness of a variance reduction simulation algorithm is measured in the following way. We calculate the product
of the necessary CPU time and the estimated variance of the estimation. This product is compared to the same for the simple
Crude Monte Carlo simulation. This was originally used for comparison of different variance reduction techniques by Hammersley
and Handscomb (Monte Carlo Methods. Methuen & Co Ltd, London, 1967). The main result of the paper is the extension of CE method
for estimation of rare event probabilities in stochastic networks with beta distributions. In this case the calculation of
reference parameters of the importance sampling distribution requires numerical solution of a nonlinear equation system. This
is done by applying a Newton–Raphson iteration scheme. In this case the CPU time spent for calculation of the reference parameter
values cannot be neglected. Numerical results will also be presented.
This work was supported by grant from the Hungarian National Scientific Research Grant OTKA
T047340. 相似文献
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本文研究既含有固定效应又含有随机效应的线性混合模型,在随机效应的方差不同即异方差情况下,即考虑方差受外界因素的影响,如温度、湿度等,我们称之为协变量,在有协变量情况下对方差建立对数线性模型,运用最大似然估计讨论了固定效应的估计和随机效应的预测,并且用约束最大似然(REML)方法研究对数线性模型中参数和随机误差中参数(离差参数)的估计,并讨论估计量的性质及离差参数估计量的渐近正态性。 相似文献
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方差估计是抽样调查的重要组成部分,在实际的抽样设计中,往往通过复杂的细分层提高样本的代表,平衡半样本方法成为方差估计的主要方法之一。本文主要阐述Fay平衡半样本方法的基本原因和应用,并对针对该方法存在的问题进行改进,最后通过一个实例模拟阐述其在实际调查中的应用。 相似文献
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本文分别在正态分布和任意分布设定下讨论最小在险价值(VaR)的风险对冲问题。在正态分布设定下,本文深入讨论最小方差对冲比率和最小VaR对冲比率的性质,并得出最小VaR对冲策略下组合收益率的均值和方差大于最小方差策略下组合收益率的均值和方差。在任意分布设定下,本文构建一种新的VaR对冲模型,该模型引入非参数核估计方法对VaR进行估计,然后基于VaR核估计量建立风险对冲问题,实现风险估计与风险对冲同步进行。实证结果非常稳健地表明,不做任何分布假设下的核估计法得到的风险对冲效果优于最小方差对冲策略和正态分布设定下的最小VaR对冲策略。 相似文献
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张忠占 《高校应用数学学报(A辑)》1993,(4):386-395
本文讨论了三参数对正态分布的参数估计问题,指出了最小二乘估计存在的问题,并提出了两种修改的最小二乘估计,模拟研究表明,这种估计较以前提出的估计有一定的优点。 相似文献
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Zheng Peng Donghua Wu Quan Zheng 《Journal of Optimization Theory and Applications》2013,156(2):493-523
In this paper, we propose a new method, namely the level-value estimation method, for finding global minimizer of continuous optimization problem. For this purpose, we define the variance function and the mean deviation function, both depend on a level value of the objective function to be minimized. These functions have some good properties when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation equals the global minimal value of the corresponding optimization problem. We also propose an implementable algorithm of the level-value estimation method where importance sampling is used to calculate integrals of the variance function and the mean deviation function. The main idea of the cross-entropy method is used to update the parameters of sample distribution at each iteration. The implementable level-value estimation method has been verified to satisfy the convergent conditions of the inexact Newton method for solving a single variable nonlinear equation. Thus, convergence is guaranteed. The numerical results indicate that the proposed method is applicable and efficient in solving global optimization problems. 相似文献