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1.
在正态-逆Wishart先验下研究了多元线性模型中参数的经验Bayes估计及其优良性问题.当先验分布中含有未知参数时,构造了回归系数矩阵和误差方差矩阵的经验Bayes估计,并在Bayes均方误差(简称BMSE)准则和Bayes均方误差阵(简称BMSEM)准则下,证明了经验Bayes估计优于最小二乘估计.最后,进行了Monte Carlo模拟研究,进一步验证了理论结果. 相似文献
2.
对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差.最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计. 相似文献
3.
《Statistics & probability letters》1985,3(6):309-313
In the empirical Bayes (EB) decision problem consisting of squared error estimation of a Poisson mean, a prior distribution λ is placed on the gamma family of prior distributions to produce Bayes EB estimators which are admissible. A subclass of such estimators is shown to be asymptotically optimal (a.o.). The results of a Monte Carlo study are presented to demonstrate the favorable a.o. property of the Bayes EB estimators in comparison with other competitors. 相似文献
4.
5.
本文获得了刻度指数族变量带误差情形下的贝叶斯决策,且利用解卷积的核方法构造出了经验贝叶斯决策.在适当的条件下,证明了经验贝叶斯决策的渐近最优性. 相似文献
6.
Empirical Bayes approach to estimation of many parameters is considered. Special features of the techniques discussed are: (i) the handling of unequal sample sizes at various stages of an Empirical Bayes sampling scheme and (ii) a general iterative procedure for estimating the parameters of a parametric prior distribution based on the likelihood approach. Linear empirical Bayes estimation is also considered. Application of the general techniques is demonstrated with special reference to a multinomial data distribution. 相似文献
7.
M. Ya. Penskaya 《Journal of Mathematical Sciences》1995,75(2):1524-1535
The usual empirical Bayes setting is considered with θ being a shift or a scale parameter. A class of empirical Bayes estimators
of a function b(θ) is proposed. The properties of the estimates are studied and mean square errors are calculated. The lower
bounds are constructed for mean square errors of the empirical Bayes estimators over the class of all empirical Bayes estimators
of b(θ). The results are applied to the case b(θ)=θ. The examples of the upper and lower bounds for mean square error are
presented for the most popular families of conditional distributions.
Added to the English translaion. 相似文献
8.
In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares(LS)estimator are investigated under mean square error matrix(MSEM)criterion. 相似文献
9.
指数分布中寿命参数的经验贝叶斯检验 总被引:1,自引:0,他引:1
本文中,我们利用经验贝叶斯方法研究了指数分布中寿命参数的检验问题.对于假设H0∶θ≤θ0 H1∶θ>θ0,在线性误差损失下,利用两种不同的核估计方法,我们获得了贝叶斯检验风险的同样上界.本文获得的收敛速度优于文献中的早期结果. 相似文献
10.
In this paper Bayesian statistical analysis of masked data is
considered based on the Pareto distribution. The likelihood function is simplified by
introducing auxiliary variables, which describe the causes of failure. Three Bayesian
approaches (Bayes using subjective priors, hierarchical Bayes and empirical Bayes) are
utilized to estimate the parameters, and we compare these methods by analyzing a real
data. Finally we discuss the method of avoiding the choice of the hyperparameters in
the prior distributions. 相似文献
11.
在线性模型中回归系数与误差方差具有正态-逆Gamma先验时,导出了回归系数与误差方差的同时Bayes估计.在均方误差矩阵准则和Bayes Pitman closeness准则下,研究了回归系数的Bayes估计相对于最小二乘(LS)估计的优良性,还讨论了误差方差的Bayes估计在均方误差准则下相对于LS估计的优良性. 相似文献
12.
??The Bayes estimators of variance components are derived under
weighted square loss function for the balanced one-way classification random effects
model with the assumption that variance component has the conjugate prior distribution.
The superiorities of the Bayes estimators for variance components to traditional ANOVA
estimators are studied in terms of the mean square error (MSE) criterion. Finally, a
remark for main results is given. 相似文献
13.
The Superiorities of Simultaneous Empirical Bayes Estimation for the Regression Coefficients and Error-Variance in Linear Model 下载免费PDF全文
When the hyperparameters of prior
distribution are partly known in linear model, the simultaneous
parametric empirical Bayes estimators (PEBE) of the regression
coefficients and error variance are constructed. The superiority of
PEBE over the least squares estimator (LSE) of regression
coefficients is investigated in terms of the the mean square error
matrix (MSEM) criterion, and the superiority of PEBE over LSE of the
error variance is discussed under the the mean square error (MSE)
criterion. Finally, when all hyperparameters are unknown, the PEBE
of regression coefficients and error variance are reconstructed and
the superiority of them over LSE under the MSE criterion are studied
by simulation methods. 相似文献
14.
Kęstutis Dučinskas 《Lithuanian Mathematical Journal》2011,51(4):477-485
We consider the problem of supervised classifying the multivariate Gaussian random field (GRF) single observation into one
of two populations in case of given training sample. The populations are specified by different regression mean models and
by common factorized covariance function. For completely specified populations, we derive a formula for Bayes error rate.
In the case of unknown regression parameters and feature covariance matrix, the plug-in Bayes discriminant function based
on ML estimators of parameters is used for classification. We derive the actual error rate and the asymptotic expansion of
the expected error rate associated with plug-in Bayes discriminant function. These results are multivariate generalizations
of previous ones. Numerical analysis of the derived formulas is implemented for the bivariate GRF observations at locations
belonging to the two-dimensional lattice with unit spacing. 相似文献
15.
错误先验假定下Bayes线性无偏估计的稳健性 总被引:1,自引:0,他引:1
本文基于错误的先验假定获得了一般线性模型下可估函数的Bayes线性无偏估计(BLUE), 证明了在均方误差矩阵(MSEM)准则和后验Pitman Closeness (PPC)准则下BLUE相对于最小二乘估计(LSE)的优良性, 并导出了它们的相对效率的界, 从而获得BLUE的稳健性. 相似文献
16.
In this paper, the empirical Bayes (EB) two-sided test for parameter of Cox models is investigated under square loss functions. At first by using recursive kernel estimation of probability function the empirical Bayes two-sided test rule is constructed. It proves that the proposed empirical Bayes test rule is asymptotic optimal and convergence rates are obtained under suitable conditions. Finally an example of satisfying theorem conditions is given. 相似文献
17.
Wang-Shu Lu 《Annals of the Institute of Statistical Mathematics》1994,46(3):497-507
A Bayesian shrinkage estimate for the mean in the generalized linear empirical Bayes model is proposed. The posterior mean under the empirical Bayes model has a shrinkage pattern. The shrinkage factor is estimated by using a Bayesian method with the regression coefficients to be fixed at the maximum extended quasi-likelihood estimates. This approach develops a Bayesian shrinkage estimate of the mean which is numerically quite tractable. The method is illustrated with a data set, and the estimate is compared with an earlier one based on an empirical Bayes method. In a special case of the homogeneous model with exchangeable priors, the performance of the Bayesian estimate is illustrated by computer simulations. The simulation result shows as improvement of the Bayesian estimate over the empirical Bayes estimate in some situations. 相似文献
18.
在对称平方损失函数下, 利用逐步增加首失效截尾样本,
研究两参数Pareto分布族参数的一致最小方差无偏估计(UMVUE),
Bayes估计和参数型经验Bayes(PEB)估计. 按照均方误差(MSE)准则,
比较UMVUE与PEB估计的优良性. 根据风险函数导出Bayes估计与PEB估计的渐近性,
并获得它们的收敛速度. 在相同的置信水平下,
研究参数分别在经典统计和Bayes统计中的区间估计,
并利用数值模拟说明Bayes区间估计的精度高于经典统计区间估计. 相似文献
19.
The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which regulates the amount of degrees of freedom used in the fit. In this paper we propose data-driven methods for selecting smoothing parameters when the targeted parameter is an average causal effect. For this purpose, we propose to estimate the exact expression of the mean squared error of the estimators. Asymptotic approximations indicate that the smoothing parameters minimizing this mean squared error converges to zero faster than the optimal smoothing parameter for the estimation of the regression functions. In a simulation study we show that the proposed data-driven methods for selecting the smoothing parameters yield lower empirical mean squared error than other methods available such as, e.g., cross-validation. 相似文献