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 first introduce semi-parametric heteroscedastic hierarchical models. Then, we define a new version of the empirical likelihood function (Restricted Joint Empirical likelihood) and use it to obtain the shrinkage estimators of the models' parameters in these models. Under different assumptions, a simulation study investigates the better performance of the restricted joint empirical likelihood function in the analysis of semi-parametric heterogeneity hierarchical models. Furthermore, we analyze an actual data set using the RJEL method.

Complex and variable nature of the river sediment yield caused many problems in prediction of the long-term sediment yield and input into the reservoirs .sediment rating curves generally used to estimate the suspended sediment load of the river and drainage basin. Since the regression equations of the sediment rating curves obtained by logarithmic retransformation and little independent variable include in this equation they also overestimate or underestimate the true load of the rivers. In this research in order to improve and develop sediment yield estimation methods the estimates of 10 kind of sediment rating curves were compared with actual loads of 5 stations in different climate zones of the country by using accuracy and precision index .the results show that in estimating long term mean load of the selected periods the Linear-MVUE sediment rating curve has relatively high accuracy and precision comparing other kinds of sediment rating curves. In average, the accuracy index of this method is about 1.23 that is reasonable among other methods. Since this kind of sediment, rating curve uses different data characteristics and information it could be recommend for application in sediment yield estimation within acceptable confidence limits.

In this paper, we propose a presmooth product-limit estimator to draw statistical inference on the unbiased distribution function representing the population of interest. The strong consistency of the estimator proposed is investigated. The finite sample performance of the proposed estimator is evaluated using simulation studies. It is observed that the proposed estimator exhibits greater efficiency in comparison with the alternative method in de Uñ a-Á lvarez (Test 11(1): 109– 125, 2002).

Power line signal are normally subjected to disturbance and noise which degrade the overall performance of power quality monitoring system. This paper proposes a modified approach for denoising by combining an algorithm known as Stein’s Unbiased Risk Estimator (SURE) algorithm incorporated with phaselet transform (PT). This algorithm is chosen particularly, as it not only performs denoising but also tends to optimally smooth the noisy signal. Since the algorithm is incorporated with phaselet, this leads to increase the coefficients obtained. Hence this method is found to be effective for application for denoising of power line signals. The different types of power quality signals simulated using the proposed method is found to be efficient and provide better results with increased Signal-to-Noise ratio (SNR) when compared with the results obtained by applying wavelet transform (WT).

Inversion of magnetic data is one of the important steps in the interpretation of practical magnetic data. The inversion result can be obtained by minimization of Tikhonov objective function. The determination of an optimal regularization parameter is highly important in magnetic data inversion. In this paper, an attempt has been made to use unbiased predictive risk estimator (UPRE) method in selecting the best regularization parameter for 3D constrained inversion of magnetic data using gradient projection reduced Newton (GPRN) algorithm. To achieve this goal, an algorithm has been developed to estimate this parameter. The validity of the proposed algorithm has been evaluated by magnetic data acquired from a synthetic model. The results have been compared with the results of generalized cross validation (GCV) method. The GCV method failed to estimate the regularization parameter, but the UPRE method could find the best regularization parameter. Then, the algorithm was used for inversion of real magnetic data obtained from Allah Abad iron deposit. The results of three-dimensional (3-D) inversion of magnetic data from this iron deposit show that the GPRN algorithm can provide an adequate estimate of magnetic susceptibility and geometry of subsurface structures of mineral deposits. A comparison of the inversion results with drilling data clearly indicate that the proposed algorithm can be used for 3-D inversion of magnetic data to estimate precisely the magnetic susceptibility and geometry of magnetized ore bodies.

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.

Some examples of absurd uniformly minimum variance unbiased estimators are discussed. Two reasons, argued in the literature, for having such estimators are lack of enough information in the available data and property of unbiasedness. In this paper, accepting both of these views, we show that an appropriate choice of loss function using a general concept of unbiasedness leads to risk unbiased, admissible and reasonable estimators. For this we extend the Rao-Blackwell theorem using a new way of defining unbiased estimator.