Simultaneous estimation of two ordered exponential parameters

TL;DR: It is proved that the best equivariant estimators of the scale parameters (in the unrestricted case) are not admissible and estimators that improve upon the usual ones are constructed (when these parameters are known to be ordered).

TL;DR: In this paper, the authors show that the isotonic regression estimator fails to dominate the unrestricted maximum likelihood estimator in terms of mean squared error, when the variances are unknown and unequal in a normal model.

TL;DR: In this paper, the hazard rate of two exponential distributions with unknown and ordered location parameters under a general class of bowl-shaped scale invariant distributions is estimated under a generalized class of scale invariants.

TL;DR: In this article, the generalized Pitman estimator of Θ with respect to the uniform prior on the restricted space Ω is considered and the risk performance of δ p is compared numerically with that of the restricted maximum likelihood estimator δ MLE and the usual estimator X 1, X 2, X 3.

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TL;DR: In this paper, Statistical Inference Under Order Restrictions (SINR) under order restrictions is discussed. But this paper is restricted to the case of order restrictions. And it is not applicable to the present paper.

TL;DR: In this paper, the authors studied the problem of estimating the largest of a set of ordered parameters, when it is known which populations correspond to each ordered parameter, and showed that the generalized Bayes estimator is admissible and minimax.

TL;DR: The problem of estimating ordered parameters is encountered in biological, agricultural, reliability and various other experiments as discussed by the authors, where the authors consider two populations with densities f1(x 1-ω1) and f2(x 2-ω2) where ω1#ω2.