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1.
Dominique Fourdrinier William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2003,55(4):803-816
We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In
3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988,
On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual
estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized
Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly,
that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax
estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes
estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator
of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss.
Research supported by NSF Grant DMS-97-04524. 相似文献
2.
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
3.
Mamikon S. Ginovyan 《Acta Appl Math》2011,115(2):233-254
The paper considers a problem of construction of asymptotically efficient estimators for functionals defined on a class of
spectral densities, and bounding the minimax mean square risks. We define the concepts of H- and IK-efficiency of estimators, based on the variants of Hájek-Ibragimov-Khas’minskii convolution theorem and Hájek-Le
Cam local asymptotic minimax theorem, respectively, and show that the simple “plug-in” statistic Φ(I
T
), where I
T
=I
T
(λ) is the periodogram of the underlying stationary Gaussian process X(t) with an unknown spectral density θ(λ), λ∈ℝ, is H- and IK-asymptotically efficient estimator for a linear functional Φ(θ), while for a nonlinear smooth functional Φ(θ) an H- and IK-asymptotically efficient estimator is the statistic F([^(q)]T)\Phi(\widehat{\theta}_{T}), where [^(q)]T\widehat{\theta}_{T} is a suitable sequence of the so-called “undersmoothed” kernel estimators of the unknown spectral density θ(λ). Exact asymptotic bounds for minimax mean square risks of estimators of linear functionals are also obtained. 相似文献
4.
M. Ya. Penskaya 《Journal of Mathematical Sciences》1995,75(2):1518-1523
The kernel estimators of a prior density function of a shift parameter are proposed. The upper and lower bounds for the mean
square error of these estimates are evaluated.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 39–46, Perm, 1991. 相似文献
5.
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
6.
In this paper, the Bayes estimator and the parametric empirical Bayes estimator (PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator (MVUE) and a revised James-Stein estimators (RJSE) are investigated respectively under mean square error (MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion. 相似文献
7.
错误先验假定下回归系数Bayes估计的小样本性质 总被引:15,自引:0,他引:15
本在于错误指定的先验假定获得了回归系数的Bayes估计(BE),并在均方误差矩阵准则下对其与最小二乘(LS)估计进行了比较,导出了它们的相对效率的界、讨论了在后验PitmanCloseness准则下BE相对于LS估计的优良性。 相似文献
8.
Radhey S. Singh Manzoor Ahmad 《Annals of the Institute of Statistical Mathematics》1987,39(1):549-562
Summary Two sets of modified kernel estimates of a regression function are proposed: one when a bound on the regression function is
known and the other when nothing of this sort is at hand. Explicit bounds on the mean square errors of the estimators are
obtained. Pointwise as well as uniform consistency in mean square and consistency in probability of the estimators are proved.
Speed of convergence in each case is investigated.
Major work of this research was completed during the first author's two visits (November–December, 1983 and August–September
1984) to the second author at the Universite du Quebec a Montreal. Part of the work of the second author was supported by
the Air Force Office of Scientific Research under contract F49620-85-C-0008 while he was at the University of Pittsburgh during
Spring in 1985. 相似文献
9.
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
10.
In this paper, we establish oracle inequalities for penalized projection estimators of the intensity of an inhomogeneous
Poisson process. We study consequently the adaptive properties of penalized projection estimators. At first we provide lower
bounds for the minimax risk over various sets of smoothness for the intensity and then we prove that our estimators achieve
these lower bounds up to some constants. The crucial tools to obtain the oracle inequalities are new concentration inequalities
for suprema of integral functionals of Poisson processes which are analogous to Talagrand's inequalities for empirical processes.
Received: 24 April 2001 / Revised version: 9 October 2002 /
Published online: 15 April 2003
Mathematics Subject Classification (2000): 60E15, 62G05, 62G07
Key words or phrases: Inhomogeneous Poisson process – Concentration inequalities – Model selection – Penalized projection estimator – Adaptive
estimation 相似文献
11.
??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
12.
M. Ya. Penskaya 《Journal of Mathematical Sciences》1996,81(4):2803-2810
Lower bounds for errors of prior density estimators are presented for a wide class of conditional densities of observations.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 77–88, Perm, 1993. 相似文献
13.
We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama, W.E. Strawderman, A new class of generalized Bayes minimax ridge regression estimators, Ann. Statist., 33 (2005) 1753–1770] to include non-monotone shrinkage functions. 相似文献
14.
Bayes minimax estimators of the mean of a scale mixture of multivariate normal distributions 总被引:1,自引:0,他引:1
Bayes estimation of the mean of a variance mixture of multivariate normal distributions is considered under sum of squared errors loss. We find broad class of priors (also in the variance mixture of normal class) which result in proper and generalized Bayes minimax estimators. This paper extends the results of Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264] in a manner similar to that of Maruyama [Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distribution, J. Multivariate Anal. 21 (2003) 69-78] but somewhat more in the spirit of Fourdrinier et al. [On the construction of bayes minimax estimators, Ann. Statist. 26 (1998) 660-671] for the normal case, in the sense that we construct classes of priors giving rise to minimaxity. A feature of this paper is that in certain cases we are able to construct proper Bayes minimax estimators satisfying the properties and bounds in Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264]. We also give some insight into why Strawderman's results do or do not seem to apply in certain cases. In cases where it does not apply, we give minimax estimators based on Berger's [Minimax estimation of location vectors for a wide class of densities, Ann. Statist. 3 (1975) 1318-1328] results. A main condition for minimaxity is that the mixing distributions of the sampling distribution and the prior distribution satisfy a monotone likelihood ratio property with respect to a scale parameter. 相似文献
15.
M. Ya. Penskaya 《Journal of Mathematical Sciences》1995,75(1):1404-1410
Given the function f and the vector-statistic tN which is a mean square consistent estimator of a parameter a, the problem is to estimate f(a). The criteria for the mean
square consistency of the estimator f(tN) are considered. In the case where the estimator f(tN) is not mean square consistent, a class of estimators of f(a) is proposed, and it is proved that the estimators of the class
are mean square consistent for all distribution of tN.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 44–55, Perm, 1990. 相似文献
16.
In the estimation problem of the mean function of an inhomogeneous Poisson process there is a class of kernel type estimators that are asymptotically efficient alongside with the empirical mean function. We start by describing such a class of estimators which we call first order efficient estimators. To choose the best one among them we prove a lower bound that compares the second order term of the mean integrated square error of all estimators. The proof is carried out under the assumption on the mean function Λ(·) that Λ(τ) = S, where S is a known positive number. In the end, we discuss the possibility of the construction of an estimator which attains this lower bound, thus, is asymptotically second order efficient. 相似文献
17.
Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval 总被引:3,自引:0,他引:3
Éric Marchand William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2005,57(1):129-143
For location families with densitiesf
0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f
0, ρ), the Bayes estimator δ
U
with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous
dominance results due to Katz and Farrell, we make use of Kubokawa'sIERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and
are characterized in terms of δ
U
. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint
of the form θ∈[a, b].
Research supported by NSERC of Canada. 相似文献
18.
单向分类随机效应模型中方差分量的渐近最优经验Bayes估计 总被引:2,自引:0,他引:2
本文在加权平方损失下导出了单向分类随机效应模型中方差分量的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,证明了 EB估计的渐近最优性.文末还给出了一个例子说明了符合定理条件的先验分布是存在 的. 相似文献
19.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):81-90
Summary It is desired to estimate a parameter
with the loss function of the formL(θ, a)=W(‖θ−a‖), where
is convex, differentiable, and non-decreasing. With this structure a characterization of Bayes estimators is given. Also
it is noted that if the sample space,
, for the observation,X, is a complete separable metric space then a Bayes estimator exists. 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