Consider estimating the common meanè of two p-variate normal populations. A Best Linear Risk Unbiased Equivariant (BLRUE) estimator under LINEX loss function was proposed when the variances are known. Also a class of shrinkage estimators was studied.

The improved estimator of the variance in the general linear model is presented under an asymmetric linex loss function.

This is a survey of a variety of equivariant (co)homology theories for operator algebras. We briefly discuss a background on equivariant Hochschild cohomology. We discuss a notion of equivariant L2-cohomology and equivariant L2-Betti numbers for subalgebras of a von Neumann algebra. For graded C ∗,-algebras (with grading over a group) we elaborate on a notion of graded L2-cohomology and its relation to equivariant L2-cohomology.

The quadratic loss function has been used by decision-theoretic statisticians and economists for many years. In this paper the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant estimator and Bayes estimators are obtained. Fisher’ s problem of the Nile as an example is included.

In this paper, we show that the unbiased estimator of the certion Parameter of the selected population does not exist. First, we give a new proof of this fact for the selected normal population. We then extend the result to some other distributions belonging to one-parameteric exponential family. Whenever an unbiased estimator exists, it is shown to be a function of order statiscs.

In this paper we propose an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of estimator is proved, and comparisons are made with Vasicek’s estimator (1976), van Es’s estimator (1992), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed estimator has smaller mean squared error than above estimators.

Due to the lack of measurement in distribution systems, state estimation has particular importance. Different methods are presented to improve the accuracy of system state with limited measurements. In this paper a new state estimator in distribution systems are offered. This estimator bases on backward forward load flow estimates system state with adjusting load consumption at each step. Voltage measurements in slack bus, loads and zero injection measurements are inputs of estimator. This estimator is compared with weight least square estimator and its results are shown. The estimator calculates voltage magnitude with less error and also faster than WLS estimator. 85-bus system is presented in this paper.

Let Xi1, …, Xini be a random sample from a gamma distribution with known shape parameter ni>0 and unknown scale parameter bi>0, i= 1, 2, satisfying 0< b1 £ b2. We consider the class of mixed estimators for estimation of b1 and b2 under reflected gamma loss function. It has been shown that the minimum risk equivariant estimator of bi, i= 1, 2, which is admissible when no information on the ordering of parameters are given, is inadmissible and dominated by a class of mixed estimators when it is known that the parameters are ordered. Also, the inadmissible estimators in the class of mixed estimators are derived. Finally the results are extended to some subclass of exponential family.