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.     

Irreconcilability of P-value and Bayesian measure in two-sided hypothesis: Pareto distribution with the presence of nuisance parameter

Abstract

This article is concerned with the comparison of Bayesian and classical testing of a point null hypothesis for the Pareto distribution when there is a nuisance parameter. In the first stage, using a fixed prior distribution, the posterior probability is obtained and compared with the P-value. In the second case, lower bounds of the posterior probability of H₀, under a reasonable class of prior distributions, are compared with the P-value. It has been shown that even in the presence of nuisance parameters for the model, these two approaches can lead to different results in statistical inference.     

Bayesian inferences and forecasts with moving averages processes

This paper will develop Bayesian inferential and forecasting techniques which can be used with any moving average process. By employing the conditional likelihood function, at-approximation to the predictive distribution and the marginal posterior distribution of the moving average parameters is developed. Several examples demonstrate posterior and predictive inferences.     

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.     

Goodness-of-Fit Test and Parameter Estimation for a Proportional Odds Model of Random Censorship

Censored data arise naturally in a number of fields, particularly in problems of reliability and survival analysis. There are several types of censoring, in this article, we will confine ourselves to the right randomly censoring type. Recently, Ahmadi et al. (2010 Ahmadi , J. , Doostparast , M. , Parsian , A. ( 2010 ). Bayes estimation based on random censored data for some life time models under symmetric and asymmetric loss functions . Communcations in Statistics-Theory and Methods , 39 : 3058 – 3071 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) considered the problem of estimating unknown parameters in a general framework based on the right randomly censored data. They assumed that the survival function of the censoring time is free of the unknown parameter. This assumption is sometimes inappropriate. In such cases, a proportional odds (PO) model may be more appropriate (Lam and Leung, 2001 Lam , K. F. , Leung , T. L. ( 2001 ). Marginal likelihood estimation for proportional odds models with right censored data . Lifetime Data Analysis 7 : 39 – 54 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Under this model, in this article, point and interval estimations for the unknown parameters are obtained. Since it is important to check the adequacy of models upon which inferences are based (Lawless, 2003 Lawless , J. F. (2003). Statistical Models and Methods for Lifetime Data. , 2nd ed. New York : John Wiley & Sons. [Google Scholar], p. 465), two new goodness-of-fit tests for PO model based on right randomly censored data are proposed. The proposed procedures are applied to two real data sets due to Smith (2002 Smith , P. J. ( 2002 ). Analysis of Failure and Survival Data . London : Chapman & Hall, CRC . [Google Scholar]). A Monte Carlo simulation study is conducted to carry out the behavior of the estimators obtained.     

A comparison of three methods of estimating the logistic regression coefficients

A Sampling experiment performed using data collected for a large clinical trial shows that the discriminant function estimates of the logistic regression coefficients for discrete variables may be severely biased. The simulations show that the mixed variable location model coefficient estimates have bias which is of the same magnitude as the bias in the coefficient estimates obtained using conditional maximum likelihood estimates but require about one-tenth of the computer time.     

Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test

We study distributional properties of generalized order statistics (gos) related by a random shift or scaling scheme in the continuous and discrete case, respectively. In the continuous case, we obtain new characterizations of distributions relating non-neighbouring gos extending some results given in the literature for the neighbouring cases. On the other hand, in the discrete case, we investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose gos are related by a random translation.     

Bayesian sample‐size determination methods considering both worthwhileness and unpromisingness for exploratory two‐arm randomized clinical trials with binary endpoints

A randomized exploratory clinical trial comparing an experimental treatment with a control treatment on a binary endpoint is often conducted to make a go or no‐go decision. Such an exploratory trial needs to have an adequate sample size such that it will provide convincing evidence that the experimental treatment is either worthwhile or unpromising relative to the control treatment. In this paper, we propose three new sample‐size determination methods for an exploratory trial, which utilize the posterior probabilities calculated from predefined efficacy and inefficacy criteria leading to a declaration of the worthwhileness or unpromisingness of the experimental treatment. Simulation studies, including numerical investigation, showed that all three methods could declare the experimental treatment as worthwhile or unpromising with a high probability when the true response probability of the experimental treatment group is higher or lower, respectively, than that of the control treatment group.