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11.
Let X
1, X
2, ..., X
n be a random sample from a normal population with mean μ and variance σ
2. In many real life situations, specially in lifetime or reliability estimation, the parameter μ is known a priori to lie in an interval [a, ∞). This makes the usual maximum likelihood estimator (MLE) ̄ an inadmissible estimator of μ with respect to the squared error loss. This is due to the fact that it may take values outside the parameter space. Katz
(1961) and Gupta and Rohatgi (1980) proposed estimators which lie completely in the given interval. In this paper we derive
some new estimators for μ and present a comparative study of the risk performance of these estimators. Both the known and unknown variance cases have
been explored. The new estimators are shown to have superior risk performance over the existing ones over large portions of
the parameter space. 相似文献
12.
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14.
In the stress–strength models, analysis is based on the reliability of the system where the system is either in operational state or in failure state. Ery?lmaz (2011) introduced the stress–strength reliability in a different framework assigning more than two states to the system depending on the difference between strength and stress values. Unlike Ery?lmaz (2011), the present article deals with the ratio of the strength and stress values when the stress and strength follow independent exponential distributions. This article presents in detail the estimation aspect of the multistate stress–strength reliability function. 相似文献
15.
Suppose we have k( ? 2) normal populations with a common mean and possibly different variances. The problem of estimation of quantile of the first population is considered with respect to a quadratic loss function. In this paper, we have generalized the inadmissibility results obtained by Kumar and Tripathy (2011) for k = 2 to a general k( ? 2). Moreover, a massive simulation study has been done in order to numerically compare the risk values of various proposed estimators for the cases k = 3 and k = 4 and recommendations are made for the use of estimators under certain situations. 相似文献
16.
Minimax estimators for the lower-bounded scale parameter of a location-scale family of distributions
This article is concerned with the minimax estimation of a scale parameter under the quadratic loss function where the family of densities is location-scale type. We obtain results for the case when the scale parameter is bounded below by a known constant. Implications for the estimation of a lower-bounded scale parameter of an exponential distribution are presented under unknown location. Furthermore, classes of improved minimax estimators are derived for the restricted parameter using the Integral Expression for Risk Difference (IERD) approach of Kubokawa (1994). These classes are shown to include some existing estimators from literature. 相似文献
17.
Abhijit Dasgupta Steven G. Self Somesh Das Gupta 《Journal of statistical planning and inference》2007
Identifiability is a primary assumption in virtually all classical statistical theory. However, such an assumption may be violated in a variety of statistical models. We consider parametric models where the assumption of identifiability is violated, but otherwise satisfy standard assumptions. We propose an analytic method for constructing new parameters under which the model will be at least locally identifiable. This method is based on solving a system of linear partial differential equations involving the Fisher information matrix. Some consequences and valid inference procedures under non-identifiability have been discussed. The method of reparametrization is illustrated with an example. 相似文献
18.
This paper is concerned with estimating the common hazard rate of two exponential distributions with unknown and ordered location parameters under a general class of bowl-shaped scale invariant loss functions. The inadmissibility of the best affine equivariant estimator is established by deriving an improved estimator. Another estimator is obtained which improves upon the best affine equivariant estimator. A class of improving estimators is derived using the integral expression of risk difference approach of Kubokawa [A unified approach to improving equivariant estimators. Ann Statist. 1994;22(1):290–299]. These results are applied to specific loss functions. It is further shown that these estimators can be derived for four important sampling schemes: (i) complete and i.i.d. sample, (ii) record values, (iii) type-II censoring, and (iv) progressive Type-II censoring. A simulation study is carried out for numerically comparing the risk performance of these proposed estimators. 相似文献
19.
AbstractIn this article, we study the problem of estimating the stress-strength reliability, where the stress and strength variables follow independent exponential distributions with a common location parameter but different scale parameters. All parameters are assumed to be unknown. We derive the MLE, the UMVUE of the reliability parameter. We also derive the Bayes estimators considering conjugate prior distributions for the scale parameters and a dependent prior for the common location parameter. Monte Carlo simulations have been carried out to compare among the proposed estimators with respect to different loss functions. 相似文献
20.
Manas Ranjan Tripathy Somesh Kumar Nabendu Pal 《Statistical Methods and Applications》2013,22(3):305-318
Independent random samples are taken from two normal populations with means $\mu _1$ and $\mu _2$ and a common unknown variance $\sigma ^2.$ It is known that $\mu _1\le \mu _2.$ In this paper, estimation of the common standard deviation $\sigma $ is considered with respect to a scale invariant loss function. A general minimaxity result is proved and a class of minimax estimators is derived. An admissibility result is proved in this class. Further a class of equivariant estimators with respect to a subgroup of affine group is considered and dominating estimators in this class are obtained. The risk performance of some of these estimators is compared numerically. 相似文献