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1.
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
2.
Wataru Sakamoto 《Computational Statistics》2007,22(4):583-597
An empirical Bayes method to select basis functions and knots in multivariate adaptive regression spline (MARS) is proposed,
which takes both advantages of frequentist model selection approaches and Bayesian approaches. A penalized likelihood is maximized
to estimate regression coefficients for selected basis functions, and an approximated marginal likelihood is maximized to
select knots and variables involved in basis functions. Moreover, the Akaike Bayes information criterion (ABIC) is used to
determine the number of basis functions. It is shown that the proposed method gives estimation of regression structure that
is relatively parsimonious and more stable for some example data sets. 相似文献
3.
A Bayesian model selection procedure for comparing models subject to inequality and/or equality constraints is proposed. An encompassing prior approach is used, and a general form of the Bayes factor of a constrained model against the encompassing model is derived. A simple estimation method is proposed which can estimate the Bayes factors for all candidate models simultaneously by using one set of samples from the encompassing model. A simulation study and a real data analysis demonstrate performance of the method. 相似文献
4.
This paper addresses the problem of estimating the normal mean matrix in the case of unknown covariance matrix. This problem is solved by considering generalized Bayesian hierarchical models. The resulting generalized Bayes estimators with respect to an invariant quadratic loss function are shown to be matricial shrinkage equivariant estimators and the conditions for their minimaxity are given. 相似文献
5.
S.R. Dalal 《Stochastic Processes and their Applications》1979,9(1):99-107
A class of random processes with invariant sample paths, that is, processes which yield (with probability one) probability distributions that are invariant under a given transformation group of interest, are introduced and their properties are studied. These processes, named Dirichlet Invariant processes, are closely related to the Dirichlet processes of Ferguson. These processes can be used as priors for Bayesian analysis of some nonparametric problems. As an application Bayes and Minimax estimates of an arbitrary distribution, symmetric about a known point, are obtained. 相似文献
6.
两参数指数-威布尔分布形状参数的经验贝叶斯估计 总被引:2,自引:1,他引:1
研究了两参数指数-威布尔分布形状参数的经验贝叶斯(EB)估计问题,并假定当其中一个形状参数α已知时,给出了另一个形状参数θ在两种不同损失函数情况下的EB估计的表达式.并运用随机模拟方法,将两种不同损失函数下的EB估计进行了比较. 相似文献
7.
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
8.
On the admissibility of an estimator of a normal mean vector under a linex loss function 总被引:7,自引:0,他引:7
Ahmad Parsian 《Annals of the Institute of Statistical Mathematics》1990,42(4):657-669
For ap-variate normal mean with known variances, the model proposed by Zellner (1986,J. Amer. Statist. Assoc.,81, 446–451) is discussed in a slightly different framework. A generalized Bayes estimate is derived from a three-stage Bayes
point of view under the asymmetric loss function, and the admissibility of such estimators is proved. 相似文献
9.
逐步增加Ⅱ型截尾下比例危险率模型的可靠性分析 总被引:1,自引:0,他引:1
基于逐步增加Ⅱ型截尾样本,分别在均方损失和Linex损失下,利用ML-Ⅱ方法研究了比例危险率模型的参数和可靠性指标的经验Bayes估计问题。为了研究估计结果的精确性,分析了一个实际应用例子,并利用Monte-Carlo方法给出一个数值模拟例子,结果表明在非对称Linex损失下,经验Bayes估计更具灵活性,且结果更加有效。 相似文献
10.
11.
利用发行的认购证有编号1,2,……,N,,本文通过随机抽取的几个认购证号码,给出了认购证发行总数的最大似然估计,一致最小方差无偏估计和Bayes估计。 相似文献
12.
Summary The Bayesian estimation on lifetime data under fuzzy environments is proposed in this paper. In order to apply the Bayesian
approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian
estimation method will be used to create the fuzzy Bayes point estimator by invoking the well-known theorem called “Resolution
Identity” in fuzzy set theory. On the other hand, we also provide computational procedures to evaluate the membership degree
of any given Bayes point estimate. In order to achieve this purpose, we transform the original problem into a nonlinear programming
problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation.
Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINDO. 相似文献
13.
M. Maswadah 《Computational Statistics》2013,28(6):2849-2859
In this study, the theory of statistical kernel density estimation has been applied for deriving non-parametric kernel prior to the empirical Bayes which frees the Bayesian inference from subjectivity that has worried some statisticians. For comparing the empirical Bayes based on the kernel prior with the fully Bayes based on the informative prior, the mean square error and the mean percentage error for the Weibull model parameters are studied based on these approaches under both symmetric and asymmetric loss functions, via Monte Carlo simulations. The results are quite favorable to the empirical Bayes that provides better estimates and outperforms the fully Bayes for different sample sizes and several values of the true parameters. Finally, a numerical example is given to demonstrate the efficiency of the empirical Bayes. 相似文献
14.
In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions, that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases. 相似文献
15.
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
16.
17.
龙兵 《数学的实践与认识》2013,43(7):104-109
首先给出了艾拉姆咖分布在定数截尾场合下参数的极大似然估计;其次由"平均剩余寿命"的概念得到了参数的拟矩估计;然后取共轭先验分布给出了参数的经验Bayes估计、区间估计及假设检验;最后通过实例给出了不同截尾样本下参数的点估计和区间估计. 相似文献
18.
The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of system reliability based on Exponential distribution by invoking the well-known theorem called “Resolution Identity” in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINGO (LINDO). 相似文献
19.
V. P. Godambe 《Annals of the Institute of Statistical Mathematics》1999,51(2):201-215
In non-Bayesian statistics, it is often realistic to replace a full distributional assumption by a much weaker assumption about its first few moments; such as for instance, mean and variance. Along the same lines in Bayesian statistics one may wish to replace a completely specified prior distribution by an assumption about just a few moments of the distribution. To deal with such Bayesian semi-parametric models defined only by a few moments, Hartigan (1969, J. Roy. Statist. Soc. Ser. B, 31, 440-454) put forward linear Bayes methodology. By now it has become a standard tool in Bayesian analysis. In this paper we formulate an alternative methodology based on the theory of optimum estimating functions. This alternative methodology is shown to be more readily applicable and efficient in common problems, than the linear Bayes methodology mentioned above. 相似文献
20.
对非平衡单向分类随机效应模型中方差分量找到了其最小充分统计量,在加权平方损失下导出了其Bayes估计,利用多元密度及其偏导数的核估计方法构造了方差分量的经验Bayes(EB)估计,并导出了其收敛速度.文末用例子说明了符合定理条件的先验分布是存在的. 相似文献