Practical bayesian approaches to the analystcs of a 2×2 contingency table with incompletely categorized data

To assess the efficacy of a treatment, patients are administered a pre-test, the treatment, and a post-test (identical to the pre-test). These patients are then categorized according to their outcomes observed on both tests,e.g., (S,S), (S,F), etc. Also, we observe "incomplete" information on the pre-tests' outcomes for some patients and the results of only the post-test being known for thers, A Bayesian framework is fit to the problem and Bayes factors, posterior odds ratios, and utility functions are given to evaluate th e treatment, A method of assessing the prior distribution is specified and a numerical example is worked.     

Some Applications of the Rao Distance to Shrinkage Estimators

Bayesian statistics is concerned with how prior information influence inferences. This article studies this problem by comparing the value of the Rao distance between prior and posterior normal distributions. Particular cases include the linear Bayes estimator, the mixed estimator, and ridge-type estimators.     

On Comparison Of Estimates Of Dispersion Using Generalized Pitman Nearness Criterion

In this paper, estimates QP dispersion matrix and its functions are compared based on generalized Pitman nearness criterion, Various Iosa functions are considered for the purpose. Locally superior estimates are defined and obtained. Comparison of these estimates are made with other standard ones. It is snown that within certain classes, defined in the paper, these are the best estimatcrs ia the generalized Fitman nearness sense     

Estimation of signal to noise ratio using mahalanobis distance

In this paper, we propose some alternative estimatiors to that given by C. G. Khatri and C. R. Rao (1985), for estimating Signal to Noise ratio. Using Pitman Nearness, Condition for prefering one estimator over the other is estabilished. It is shown numerically that estimators corresponding to Entropy loss function are better more oftern than those corresponding to Squared Error loss.     

Sequential estimation problems for negative exponential populations

The literature on sequential estimation problems for negative exponential populations has been reviewed here, We attempt to bring in all the published and unpublished materials known to us in a fairly coherent fashion. Both the concepts and theoretical findings are discussed.     

On shrinkage m-estimators of location parameters

For a general class of continuous ( and marginally symmetric ) inultivariate distributions, based on suitable M-statistics ( involving bounded but possibly discontinuous score generating functions), shrinkage estimators of location are considered. These estimators are based on the James-Stein type rule and incorporates the idea of preliminary test estimation too. The main emphasis is laid on the study of asymptotic tdistributional ) risk properties of these est-innators, and asymptotic tin-) adraissibility results are also studied under fairly general regularity conditions.     

Reconsideration of the F-test of the analysis of variance: the semi-bayesian significance test

The usual F-test of the analysis of variance is reconsidered within the Bayesian framework, In terms of predictive distributions, This leads to the notion of semi-Bayesian significance test, so called because it consists in only probabilizing the space of nuisance parameters, thus bringing a general principle for “eliminating” nuisance parameters, or more exactly incorporating information about these parameters. The approach is shown to extend the F-tests, by allowing the testing of hypotheses of non-zero effects.     

Reliability Characteristics of the Maxwell Distribution: A Bayes Estimation Study

ABSTRACT

This article presents maximum likelihood, Bayes, and empirical Bayes estimators of the truncated first moment and hazard function of the Maxwell distribution. A comparison of the relative efficiency of these three estimators is performed via a Monte Carlo simulation study.     

Estimation of Dynamic Bivariate Mixture Models

This note compares a Bayesian Markov chain Monte Carlo approach implemented by Watanabe with a maximum likelihood ML approach based on an efficient importance sampling procedure to estimate dynamic bivariate mixture models. In these models, stock price volatility and trading volume are jointly directed by the unobservable number of price-relevant information arrivals, which is specified as a serially correlated random variable. It is shown that the efficient importance sampling technique is extremely accurate and that it produces results that differ significantly from those reported by Watanabe.     

Ridge regression estimators in the linear regression models with non-spherical errors

The present paper considers a family of ordinary ridge regression estimators in the linear regression model when the disturbances covariance matrix depends upon a few unknown parameters. An asymptotic expansion for the distribution of the ridge regression estimator is developed and under the quadratic loss function its asymptotic risk is compared with that of the feasible GLS estimator.