In this paper the classical estimators of the shape parameter for the Burr Type XII distribution, such as, the Maximum Likelihood Estimator (MLE), the Uniformly Minimum Variance Unbiased Estimator (UMVUE), and the Minimum Mean Squared Error (MinMSE) estimator are obtained. Then the problem of finding the minimax estimators of this parameter under the squared log error, precautionary, and weight...

In this study, we study the empirical Bayes estimation of the parameter of the exponential distribution. In the empirical Bayes procedure, we employ the non-parameter polynomial density estimator to the estimation of the unknown marginal probability density function, instead of estimating the unknown prior probability density function of the parameter. Empirical Bayes estimators are derived for...

in this paper, a bayesian approach is proposed for shift point detection in an inverse gaussian distribution. in this study, the mean parameter of inverse gaussian distribution is assumed to be constant and shift points in shape parameter is considered. first the posterior distribution of shape parameter is obtained. then the bayes estimators are derived under a class of priors and using variou...

The problem of estimating the parameter θ, when it is restricted to an interval of the form [ ,1] m , in a class of discrete distributions, including Binomial ( , ), k θ Negative Binomial ( , ), r θ discrete Weibull ( ) θ and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of , θ with respect to a two points boundary supported prior is minimax unde...

We consider the problem of the optimal loss functions for predicted clickthrough rates in auctions for online advertising. While standard loss functions such as mean squared error or the log likelihood loss function severely penalize large mispredictions while imposing little penalty on smaller mistakes, we nd that a loss function re ecting the true underlying economic loss resulting from mispr...

Abstract: The U, V method of estimation provides unbiased estimators or predictors of random quantities. The method was introduced by Robbins [3] and subsequently studied in a series of papers by Robbins and Zhang. (See Zhang [5].) Practical applications of the method are featured in these papers. We demonstrate that for one U function (one for which there is an important application) the V est...