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1.
Adarsha Kumar Jena 《统计学通讯:理论与方法》2019,48(14):3570-3585
The problem of estimating ordered quantiles of two exponential populations is considered, assuming equality of location parameters (minimum guarantee times), using the quadratic loss function. Under order restrictions, we propose new estimators which are the isotonized version of the MLEs, call it, restricted MLE. A sufficient condition for improving equivariant estimators is derived under order restrictions on the quantiles. Consequently, estimators improving upon the old estimators have been derived. A detailed numerical study has been done to evaluate the performance of proposed estimators using the Monte-Carlo simulation method and recommendations have been made for the use of the estimators. 相似文献
2.
This paper concludes our comprehensive study on point estimation of model parameters of a gamma distribution from a second-order decision theoretic point of view. It should be noted that efficient estimation of gamma model parameters for samples ‘not large’ is a challenging task since the exact sampling distributions of the maximum likelihood estimators and its variants are not known. Estimation of a gamma scale parameter has received less attention from the earlier researchers compared to shape parameter estimation. What we have observed here is that improved estimation of the shape parameter does not necessarily lead to improved scale estimation if a natural moment condition (which is also the maximum likelihood restriction) is satisfied. Therefore, this work deals with the gamma scale parameter estimation as a separate new problem, not as a by-product of the shape parameter estimation, and studies several estimators in terms of second-order risk. 相似文献
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In this paper we address the problem of simultaneous estimation of location parameters of several exponential distributions assuming that the scale parameters are unknown and possibly unequal. From a decision theoretic point of view it is shown that the standard estimators are inadmissible and the improved estimators are obtained when p, the number of populations, is more than one. 相似文献
6.
Summary A standard improper prior for the parameters of a MANOVA model is shown to yield an inference that is incoherent in the sense
of Heath and Sudderth. The proof of incoherence is based on the fact that the formal Bayes estimate, sayδ
0
, of the covariance matrix based on the improper prior and a certain bounded loss function is uniformly inadmissible in that
there is another estimatorδ
l
and an ɛ>0 such that the risk functions satisfyR(δ
l
,Σ)⩽R δ
0
,Σ)−ε for all values of the covariance matrix Σ. The estimatorδ
I
is formal Bayes for an alternative improper prior which leads to a coherent inference.
Research supported by National Science Foundation grants DMS-89-22607 (for Eaton) and DMS-9123358 (for Sudderth). 相似文献
7.
Martin Bilodeau 《Revue canadienne de statistique》1988,16(2):169-174
This note is an extension of Das Gupta's results (1986) on the estimation of multiparameter gamma distribution. Consider p (p ? 2) independent positive random variables with possibly different scale-parameter densities. For the estimation of the powers of the scale parameters it is shown that the “best multiple estimator” is inadmissible with respect to a large class of weighted quadratic loss functions. 相似文献
8.
Pranab Kumar Sen 《统计学通讯:理论与方法》2013,42(7):2245-2266
In multi-parameter ( multivariate ) estimation, the Stein rule provides minimax and admissible estimators , compromising generally on their unbiasedness. On the other hand, the primary aim of jack-knifing is to reduce the bias of an estimator ( without necessarily compromising on its efficacy ), and, at the same time, jackknifing provides an estimator of the sampling variance of the estimator as well. In shrinkage estimation ( where minimization of a suitably defined risk function is the basic goal ), one may wonder how far the bias-reduction objective of jackknifing incorporates the dual objective of minimaxity ( or admissibility ) and estimating the risk of the estimator ? A critical appraisal of this basic role of jackknifing in shrinkage estimation is made here. Restricted, semi-restricted and the usual versions of jackknifed shrinkage estimates are considered and their performance characteristics are studied . It is shown that for Pitman-type ( local ) alternatives, usually, jackkntfing fails to provide a consistent estimator of the ( asymptotic ) risk of the shrinkage estimator, and a degenerate asymptotic situation arises for the usual fixed alternative case. 相似文献
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The problem of estimating the common mean μ of two univariate normal populations with unknown and unequal variances is considered from a decision-theoretic point of view. We restrict our attention to an appropriate class C and its three subclasses C0C1C2of un-biased estimates of μ. We consider the usual estimate μ0 of μ which is the weighted linear combination of the sample means with weights as reciprocals of the sample variances. Its admissibility in C0 and extended admissibility in C is proved. Admissible estimates in C1 and C2are also obtained.The loss is always assumed to be squared error. The question of admissibility of μ0 in the class of all estimators is still open. 相似文献