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| Author | : Shanti S. Gupta |
| Publisher | : |
| Total Pages | : 25 |
| Release | : 1983 |
| Genre | : |
| ISBN | : |
Download On Bayes and Empirical Bayes Rules for Selecting Good Populations Book in PDF, ePub and Kindle
This paper deals with the problems of selecting all populations which are close to a control or standard. A general Bayes rule for the above problem is derived. Empirical Bayes rules are derived when the populations are assumed to be uniformly distributed. Under some conditions on the marginal and prior distributions, the rate of convergence of the empirical Bayes risk to the minimum Bayes risk is investigated. (Author).
| Author | : Shanti Swarup Gupta |
| Publisher | : |
| Total Pages | : 21 |
| Release | : 1981 |
| Genre | : Bayesian statistical decision theory |
| ISBN | : |
Download Empirical Bayes Rules for Selecting Good Populations Book in PDF, ePub and Kindle
A problem of selecting populations better than a control is considered. When the populations are uniformly distributed, empirical Bayes rules are derived for a linear loss function for both the known control parameter and the unknown control parameter cases. When the priors are assumed to have bounded supports, empirical Bayes rules for selecting good populations are derived for distributions with truncation parameters (i.e. the form of the pdf is f(x/theta) = Pi(x)ci(theta)I(O, theta)(x)). Monte Carlo studies are carried out which determine the minimum sample sizes needed to make the relative errors less than epsilon for given epsilon-values. (Author).
| Author | : S. S. Gupta |
| Publisher | : |
| Total Pages | : 32 |
| Release | : 1984 |
| Genre | : |
| ISBN | : |
Download Empirical Bayes Rules for Selecting Good Binomial Populations Book in PDF, ePub and Kindle
This paper deals with the problem of selecting good binomial populations compared with a standard or a control through the empirical Bayes approach. Two cases have been studied: one is that the prior distribution is completely unknown and the other is that the prior distribution is symmetrical about p = 1/2, but its form is still unknown. In each case, empirical Bayes rules are derived and the rate of convergence of corresponding empirical Bayes rules is also studied.
| Author | : Shanti S. Gupta |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1985 |
| Genre | : |
| ISBN | : |
Download Empirical Bayes Rules for Selecting Good Binomial Populations. Revision Book in PDF, ePub and Kindle
This paper deals with the problem of selecting good binomial populations compared with a standard or a control through the empirical Bayes approach. Two cases have been studied: one with the pior distribution completely unknown and the other with the prior distribution symmetrical about p = 1/2, but otherwise unknown. In each case, empirical Bayes rules are derived and their rates of convergence are shown to be of order O(exp( -cn)) for some c>O, where n is the number of accumulated post experiences at hand. Keywords: Statistical decision theory; Smoothing(Mathematics); Asymptotically optimal. (Author).
| Author | : Shanti S. Gupta |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
Download Empirical Bayes Rules for Selecting the Best Binomial Population Book in PDF, ePub and Kindle
Some selection rules based on monotone empirical Bayes estimators of the binomial parameters are proposed. First, it is shown that, under the squared error loss, the Bayes risks of the proposed monotone empirical Bayes estimators converge to the related minimum Bayes risks with rates of convergence at least of order 0(nsub -n), where n is the number of accumulated past experiences at hand. Further, for the selection problem, the rates of convergence of the proposed selection rules are shown to be at least of order 0(exp( -cn)) for some c> 0. Keywords: Asymptotically optimal.
| Author | : S. S. Gupta |
| Publisher | : |
| Total Pages | : 29 |
| Release | : 1984 |
| Genre | : |
| ISBN | : |
Download Empirical Bayes Rulesfor Selecting Good Binomial Populations Book in PDF, ePub and Kindle
| Author | : Yimin Ma |
| Publisher | : |
| Total Pages | : 54 |
| Release | : 1994 |
| Genre | : Bayesian statistical decision theory |
| ISBN | : |
Download Empirical Bayes Rules for Selecting the Best Hypergeometric Population and the Best Hypergeometric Population Compared with a Control Book in PDF, ePub and Kindle
| Author | : Shanti S. Gupta |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 1988 |
| Genre | : |
| ISBN | : |
Download On Empirical Bayes Selection Rules for Negative Binomial Populations Book in PDF, ePub and Kindle
This paper deals with the problem of selecting good negative binomial populations as compared with a standard or a control. The main results are based on the use of the empirical Bayes approach. First the authors derive the monotone empirical Bayes estimators of the concerned parameters. Based on these estimators, they construct monotone empirical Bayes selection rules. Asymptotic optimality properties of the monotone empirical Bayes estimators and the monotone empirical Bayes selection rules are investigated. The respective convergence rates for the estimation problem and for the selection problem are studied, under some conditions. (KR).
| Author | : |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2001 |
| Genre | : |
| ISBN | : |
Download On Empirical Bayes Procedures for Selecting Good Populations in Positive Exponential Family Book in PDF, ePub and Kindle
The problem of selecting good ones compared with a control from k(greater than or equal to 2) positive exponential family populations is considered in this paper. A nonparametric empirical Bayes approach is used to construct the selection procedures. It has been shown that the risks of the empirical Bayes procedures converge to the (minimum) Bayes risk with a rate of O(1/n), where n is the number of accumulated past observations at hand. Simulations were carried out to study the performance of the procedures for small to moderate values of n. The results of this study are provided in the paper.
| Author | : S. S. Gupta |
| Publisher | : |
| Total Pages | : 22 |
| Release | : 1996 |
| Genre | : |
| ISBN | : |
Download Selecting Good Exponential Populations Compared with a Control Book in PDF, ePub and Kindle
