Abstract: This paper is the first of two on the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. In this paper a Bayesian analysis of this problem is presented, the optimal properties of the Bayes estimators are discussed, and as an example of the formalism, closed form expressions for the Bayes estimators for the moments of the S...

‎Consider an estimation problem in a one-parameter non-regular distribution when both endpoints of the support depend on a single parameter‎. ‎In this paper‎, ‎we give sufficient conditions for a generalized Bayes estimator of a parametric function to be admissible‎. ‎Some examples are given‎. ‎

An example was given in the textbook All of Statistics (Wasserman, 2004, pages 186-188) for arguing that, in the problems with a great many parameters Bayesian inferences are weak, because they rely heavily on the likelihood function that captures information of only a tiny fraction of the total parameters. Alternatively he suggested non-Bayesian Horwitz-Thompson estimator, which cannot be obta...

We propose an empirical Bayes method for variable selection and coefficient estimation in linear regression models. The method is based on a particular hierarchical Bayes formulation, and the empirical Bayes estimator is shown to be closely related to the LASSO estimator. Such a connection allows us to take advantage of the recently developed quick LASSO algorithm to compute the empirical Bayes...

The two-stage least-squares (2SLS) estimator is known to be biased when its first-stage fit is poor. I show that better first-stage prediction can alleviate this bias. In a two-stage linear regression model with Normal noise, I consider shrinkage in the estimation of the first-stage instrumental variable coefficients. For at least four instrumental variables and a single endogenous regressor, I...

• In the present paper we study the performance of the Bayes Shrinkage estimators for the scale parameter of the Weibull distribution under the squared error loss and the LINEX loss functions in the presence of a prior point information of the scale parameter when Type-II censored data are available. The properties of the minimax estimators are also discussed. Key-Words: • Bayes shrinkage estim...

The aim of this paper is to study the estimation of parameter of Burr Type XI distribution on the basis of lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes and empirical Bayes estimators of the unknown parameter are derived under entropy loss function. Finally, the admissibility and inadmissibility of a class of in...

Consider the problem of estimating a parametric function when the loss is quadratic. Given an improper prior distribution, there is a formal Bayes estimator for the parametric function. Associated with the estimation problem and the improper prior is a symmetric Markov chain. It is shown that if the Markov chain is recurrent, then the formal Bayes estimator is admissible. This result is used to...

in this research, an iterative approach is employed to recognize and classify control chart patterns. to do this, by taking new observations on the quality characteristic under consideration, the maximum likelihood estimator of pattern parameters is first obtained and then the probability of each pattern is determined. then using bayes’ rule, probabilities are updated recursively. finally, when...

generally, the presence of noise in geophysical measurements is inevitable and depending on the type and the level it affects the results of geophysical studies. so, denoising is an important part of the processing of geophysical data. on the other hand, geophysicists make inferences about the physical properties of the earth interior based on the indirect measurements (data) collected at or ne...