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1.
Xian Zhou Xiaoqian Sun Jinglong Wang 《Annals of the Institute of Statistical Mathematics》2001,53(4):760-768
Let X
1, , X
n
(n > p) be a random sample from multivariate normal distribution N
p
(, ), where R
p
and is a positive definite matrix, both and being unknown. We consider the problem of estimating the precision matrix –1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of –1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators. 相似文献
2.
Tatsuya Kubokawa Yoshihiko Konno 《Annals of the Institute of Statistical Mathematics》1990,42(2):331-343
For estimating the power of a generalized variance under a multivariate normal distribution with unknown means, the inadmissibility of the best affine equivariant estimator relative to the symmetric loss is shown, and a class of improved estimators is given. The problem of estimating the covariance matrix is also discussed. 相似文献
3.
Summary Estimation-preceded-by-testing is studied in the context of estimating the mean vector of a multivariate normal distribution
under squared error loss together with a complexity cost. It is shown that although the preliminary test estimator is admissible
for the univariate problem (cf Meeden and Arnold (1979),J. Amer. Statist. Assoc.,74, 872–874), for dimensionp≧3, the estimator is inadmissible. A new preliminary test estimator is obtained, which depends on the cost for each component
and dominates the usual preliminary test estimator.
Research partially supported by the NSF Grant Number DMS-82-18091 and partially by the DSR Research Development Award, University
of Florida. 相似文献
4.
In this paper, we introduce the star-shape models, where the precision matrix Ω (the inverse of the covariance matrix) is
structured by the special conditional independence. We want to estimate the precision matrix under entropy loss and symmetric
loss. We show that the maximal likelihood estimator (MLE) of the precision matrix is biased. Based on the MLE, an unbiased
estimate is obtained. We consider a type of Cholesky decomposition of Ω, in the sense that Ω=Ψ′Ψ, where Ψ is a lower triangular
matrix with positive diagonal elements. A special group
, which is a subgroup of the group consisting all lower triangular matrices, is introduced. General forms of equivariant estimates
of the covariance matrix and precision matrix are obtained. The invariant Haar measures on
, the reference prior, and the Jeffreys prior of Ψ are also discussed. We also introduce a class of priors of Ψ, which includes
all the priors described above. The posterior properties are discussed and the closed forms of Bayesian estimators are derived
under either the entropy loss or the symmetric loss. We also show that the best equivariant estimators with respect to
is the special case of Bayesian estimators. Consequently, the MLE of the precision matrix is inadmissible under either entropy
or symmetric loss. The closed form of risks of equivariant estimators are obtained. Some numerical results are given for illustration.
The project is supported by the National Science Foundation grants DMS-9972598, SES-0095919, and SES-0351523, and a grant
from Federal Aid in Wildlife Restoration Project W-13-R through Missouri Department of Conservation. 相似文献
5.
In this article, we consider the problem of estimating a p-variate (p ≥ 3) normal mean vector in a decision-theoretic setup. Using a simple property of the noncentral chi-square distribution, we have produced a sequence of smooth estimators dominating the James-Stein estimator and each improved estimator is better than the previous one. It is also shown by using a technique of [5]. J. Multivariate Anal.36 121–126) that our smooth estimators can be dominated by non-smooth estimators. 相似文献
6.
In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L(θ, δ) = v(θ/δ + δ/θ - 2). An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved. The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT(X) + d are given, where T(X) Gamma(v, θ). 相似文献
7.
Tatsuya Kubokawa 《Annals of the Institute of Statistical Mathematics》1994,46(1):95-116
The problems of estimating ratio of scale parameters of two distributions with unknown location parameters are treated from a decision-theoretic point of view. The paper provides the procedures improving on the usual ratio estimator under strictly convex loss functions and the general distributions having monotone likelihood ratio properties. In particular,double shrinkage improved estimators which utilize both of estimators of two location parameters are presented. Under order restrictions on the scale parameters, various improvements for estimation of the ratio and the scale parameters are also considered. These results are applied to normal, lognormal, exponential and pareto distributions. Finally, a multivariate extension is given for ratio of covariance matrices. 相似文献
8.
Tatsuya Kubokawa 《Journal of multivariate analysis》1998,67(2):169-189
The problem of estimating the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It is, nevertheless, established that the FGLS estimators are inadmissible in light of minimizing the covariance matrices if the dimension of the common regression coefficients is greater than or equal to three. Double shrinkage unbiased estimators are proposed as possible candidates of improved procedures. 相似文献
9.
P. Vellaisamy 《Annals of the Institute of Statistical Mathematics》1992,44(3):551-562
Suppose a subset of populations is selected from the given k gamma G(
i,p
) (i = 1,2,...,k)populations, using Gupta's rule (1963, Ann. Inst. Statist. Math., 14, 199–216). The problem of estimating the average worth of the selected subset is first considered. The natural estimator is shown to be positively biased and the UMVUE is obtained using Robbins' UV method of estimation (1988, Statistical Decision Theory and Related Topics IV, Vol. 1 (eds. S. S. Gupta and J. O. Berger), 265–270, Springer, New York). A class of estimators that dominate the natural estimator for an arbitrary k is derived. Similar results are observed for the simultaneous estimation of the selected subset. 相似文献
10.
Tatsuya Kubokawa 《Annals of the Institute of Statistical Mathematics》1988,40(3):555-563
Consider the problem of constructing an estimator with a preassigned bound on the risk for a mean of a normal distribution. The paper shows that the usual two-stage estimator is improved on by combined estimators when additional samples taken from distributions with the same mean and different variances are available. 相似文献