共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper treats the problem of estimating the restricted means of normal distributions with a known variance, where the means are restricted to a polyhedral convex cone which includes various restrictions such as positive orthant, simple order, tree order and umbrella order restrictions. In the context of the simultaneous estimation of the restricted means, it is of great interest to investigate decision-theoretic properties of the generalized Bayes estimator against the uniform prior distribution over the polyhedral convex cone. In this paper, the generalized Bayes estimator is shown to be minimax. It is also proved that it is admissible in the one- or two-dimensional case, but is improved on by a shrinkage estimator in the three- or more-dimensional case. This means that the so-called Stein phenomenon on the minimax generalized Bayes estimator can be extended to the case where the means are restricted to the polyhedral convex cone. The risk behaviors of the estimators are investigated through Monte Carlo simulation, and it is revealed that the shrinkage estimator has a substantial risk reduction. 相似文献
2.
Consider p independent distributions each belonging to the one parameter exponential family with distribution functions absolutely continuous with respect to Lebesgue measure. For estimating the natural parameter vector with p ≥ p0 (p0 is typically 2 or 3), a general class of estimators dominating the minimum variance unbiased estimator (MVUE) or an estimator which is a known constant multiple of the MVUE is produced under different weighted squared error losses. Included as special cases are some results of Hudson [13] and Berger [5]. Also, for a subfamily of the general exponential family, a class of estimators dominating the MVUE of the mean vector or an estimator which is a known constant multiple of the MVUE is produced. The major tool is to obtain a general solution to a basic differential inequality. 相似文献
3.
It is already known that the uniformly minimum variance unbiased (UMVU) estimator of the generalized variance always exists
for any natural exponential family. However, in practice, this estimator is often difficult to obtain. This paper provides
explicit forms of the UMVU estimators for the bivariate and symmetric multivariate gamma models, which are diagonal quadratic
exponential families. For the non-independent multivariate gamma models, it is shown that the UMVU and the maximum likelihood
estimators are not proportional.
相似文献
4.
In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to handle the different levels independently. The search for parameters is carried out using sample average approximation, which basically consists in applying deterministic optimisation techniques to a Monte Carlo approximation rather than resorting to stochastic approximation. Our innovative estimator leads to a robust and efficient procedure reducing both the discretization error (the bias) and the variance for a given computational effort. In the setting of discretized diffusions, we prove that our estimator satisfies a strong law of large numbers and a central limit theorem with optimal limiting variance, in the sense that this is the variance achieved by the best importance sampling measure (among the class of changes we consider), which is however non tractable. Finally, we illustrate the efficiency of our method on several numerical challenges coming from quantitative finance and show that it outperforms the standard MLMC estimator. 相似文献
5.
High breakdown estimators for principal components: the projection-pursuit approach revisited 总被引:1,自引:0,他引:1
Christophe Croux 《Journal of multivariate analysis》2005,95(1):206-226
Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with maximal variance, and their approach consists of replacing this variance by a robust scale measure. Li and Chen showed that this estimator is consistent, qualitative robust and inherits the breakdown point of the robust scale estimator. We complete their study by deriving the influence function of the estimators for the eigenvectors, eigenvalues and the associated dispersion matrix. Corresponding Gaussian efficiencies are presented as well. Asymptotic normality of the estimators has been treated in a paper of Cui et al. (Biometrika 90 (2003) 953), complementing the results of this paper. Furthermore, a simple explicit version of the projection-pursuit based estimator is proposed and shown to be fast to compute, orthogonally equivariant, and having the maximal finite-sample breakdown point property. We will illustrate the method with a real data example. 相似文献
6.
《Stochastic Processes and their Applications》2020,130(1):20-46
We develop importance sampling estimators for Monte Carlo pricing of European and path-dependent options in models driven by Lévy processes. Using results from the theory of large deviations for processes with independent increments, we compute an explicit asymptotic approximation for the variance of the pay-off under a time-dependent Esscher-style change of measure. Minimizing this asymptotic variance using convex duality, we then obtain an importance sampling estimator of the option price. We show that our estimator is logarithmically optimal among all importance sampling estimators. Numerical tests in the variance gamma model show consistent variance reduction with a small computational overhead. 相似文献
7.
Puntanen[1]提出用均方误差来度量最小二乘估计的精度,以后Styan[2],Rao[3]等相继讨论了这种精度及其界限.本文考虑采用广义方差,从而引进了一种新的最小二乘估计精度的度量并讨论了它的界. 相似文献
8.
9.
10.
We introduce a treatment of parametric estimation in which optimality of an estimator is measured in probability rather than in variance (the measure for which the strongest general results are known in statistics). Our motivation is
that the quality of an approximation algorithm is measured by the probability that it fails to approximate the desired quantity
within a set tolerance. We concentrate on the Gaussian distribution and show that the sample mean is the unique “best” estimator,
in probability, for the mean of a Gaussian distribution. We also extend this method to general penalty functions and to multidimensional
spherically symmetric Gaussians.
The algorithmic significance of studying the Gaussian distribution is established by showing that determining the average
matching size in a graph is #P-hard, and moreover approximating it reduces to estimating the mean of a random variable that (under some mild conditions)
has a distribution closely approximating a Gaussian. This random variable is (essentially) polynomial time samplable, thereby
yielding an FPRAS for the problem. 相似文献
11.
12.
本文提出方差分量ANOVA估计的一种改进方法, 证明了对于一般的方差分量模型, 只要方差分量的ANOVA估计存在就可以通过此方法给出其改进形式, 并且在均方误差意义下优于ANOVA估计. 特别地, 对于单向分类随机效应模型, Kelly和Mathew[1]对ANOVA估计的改进就是我们提出的改进方法的特殊形式, 这也给出了此类改进估计在均方误差意义下优于ANOVA估计的另一种合理的解释. 同时, 本文又将此思想应用到对谱分解估计的改进上. 本文应用协方差的简单性质证明了对带有一个随机效应的方差分量模型, 当随机效应的协方差阵只有一个非零特征值时, 随机效应方差分量谱分解估计在均方误差意义下总是优于ANOVA估计. 本文最后将第三节的结论推广到广义谱分解估计下, 同时给出广义谱分解估计待定系数的一个合理的取值. 相似文献
13.
Variance function estimation in multivariate nonparametric regression with fixed design 总被引:2,自引:0,他引:2
Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established in the iid Gaussian case. Our work uses the approach that generalizes the one used in [A. Munk, Bissantz, T. Wagner, G. Freitag, On difference based variance estimation in nonparametric regression when the covariate is high dimensional, J. R. Stat. Soc. B 67 (Part 1) (2005) 19-41] for the constant variance case. As is the case when the number of dimensions d=1, and very much contrary to standard thinking, it is often not desirable to base the estimator of the variance function on the residuals from an optimal estimator of the mean. Instead it is desirable to use estimators of the mean with minimal bias. Another important conclusion is that the first order difference based estimator that achieves minimax rate of convergence in the one-dimensional case does not do the same in the high dimensional case. Instead, the optimal order of differences depends on the number of dimensions. 相似文献
14.
对于平衡线性混合模型,本文提出了一组易验证的条件,在此条件下,方差分量的谱分解估计、方 差分析估计和最小范数二次无偏估计都相等且为一致最小方差无偏估计.同时证明了在此条件下,似然 方程和限制似然方程都有显式解,还给出了许多满足这组条件的平衡线性混合模型的例子. 相似文献
15.
Hisayuki Hara 《Journal of multivariate analysis》2001,77(2):175
It is well known that the best equivariant estimator of the variance covariance matrix of the multivariate normal distribution with respect to the full affine group of transformation is not even minimax. Some minimax estimators have been proposed. Here we treat this problem in the framework of a multivariate analysis of variance (MANOVA) model and give other classes of minimax estimators. 相似文献
16.
I. D. Coope 《Computational Optimization and Applications》1993,2(4):337-341
The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored. 相似文献
17.
Maryam Amir Haeri Mohammad Mehdi Ebadzadeh 《Fuzzy Optimization and Decision Making》2014,13(3):287-318
Mutual Information (MI) is an important dependency measure between random variables, due to its tight connection with information theory. It has numerous applications, both in theory and practice. However, when employed in practice, it is often necessary to estimate the MI from available data. There are several methods to approximate the MI, but arguably one of the simplest and most widespread techniques is the histogram-based approach. This paper suggests the use of fuzzy partitioning for the histogram-based MI estimation. It uses a general form of fuzzy membership functions, which includes the class of crisp membership functions as a special case. It is accordingly shown that the average absolute error of the fuzzy-histogram method is less than that of the naïve histogram method. Moreover, the accuracy of our technique is comparable, and in some cases superior to the accuracy of the Kernel density estimation (KDE) method, which is one of the best MI estimation methods. Furthermore, the computational cost of our technique is significantly less than that of the KDE. The new estimation method is investigated from different aspects, such as average error, bias and variance. Moreover, we explore the usefulness of the fuzzy-histogram MI estimator in a real-world bioinformatics application. Our experiments show that, in contrast to the naïve histogram MI estimator, the fuzzy-histogram MI estimator is able to reveal all dependencies between the gene-expression data. 相似文献
18.
We consider in this paper the use of Monte Carlo simulation to numerically approximate the asymptotic variance of an estimator
of a population parameter. When the variance of an estimator does not exist in finite samples, the variance of its limiting
distribution is often used for inferences. However, in this case, the numerical approximation of asymptotic variances is less
straightforward, unless their analytical derivation is mathematically tractable. The method proposed does not assume the existence
of variance in finite samples. If finite sample variance does exist, it provides a more efficient approximation than the one
based on the convergence of finite sample variances. Furthermore, the results obtained will be potentially useful in evaluating
and comparing different estimation procedures based on their asymptotic variances for various types of distributions. The
method is also applicable in surveys where the sample size required to achieve a fixed margin of error is based on the asymptotic
variance of the estimator. The proposed method can be routinely applied and alleviates the complex theoretical treatment usually
associated with the analytical derivation of the asymptotic variance of an estimator which is often managed on a case by case
basis. This is particularly appealing in view of the advance of modern computing technology. The proposed numerical approximation
is based on the variances of a certain truncated statistic for two selected sample sizes, using a Richardson extrapolation
type formulation. The variances of the truncated statistic for the two sample sizes are computed based on Monte Carlo simulations,
and the theory for optimizing the computing resources is also given. The accuracy of the proposed method is numerically demonstrated
in a classical errors-in-variables model where analytical results are available for the purpose of comparisons. 相似文献
19.
Peter Bode 《商业与工业应用随机模型》2013,29(3):187-198
During the sampling of particulate mixtures, samples taken are analyzed for their mass concentration, which generally has non‐zero sample‐to‐sample variance. Bias, variance, and mean squared error (MSE) of a number of variance estimators, derived by Geelhoed, were studied in this article. The Monte Carlo simulation was applied using an observable first‐order Markov Chain with transition probabilities that served as a model for the sample drawing process. Because the bias and variance of a variance estimator could depend on the specific circumstances under which it is applied, Monte Carlo simulation was performed for a wide range of practically relevant scenarios. Using the ‘smallest mean squared error’ as a criterion, an adaptation of an estimator based on a first‐order Taylor linearization of the sample concentration is the best. An estimator based on the Horvitz–Thompson estimator is not practically applicable because of the potentially high MSE for the cases studied. The results indicate that the Poisson estimator leads to a biased estimator for the variance of fundamental sampling error (up to 428% absolute value of relative bias) in case of low levels of grouping and segregation. The uncertainty of the results obtained by the simulations was also addressed and it was found that the results were not significantly affected. The potentials of a recently described other approach are discussed for extending the first‐order Markov Chain described here to account also for higher levels of grouping and segregation. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
20.
均匀设计抽样的应用 总被引:3,自引:0,他引:3
王兆军 《高校应用数学学报(A辑)》1997,(3):299-310
均匀设计抽样是张润楚和王兆军提出的,并且张润楚和王兆军从理论上证明了它的优良性质。本文考虑了均匀设计抽样在求函数的最大值,积分的近似计算,回归直线的拟合和极大似然估计的求取方面的应用。模拟的结果再次说明了均匀设计抽样的优良性。 相似文献