Indifference-zone ranking and selection: confidence intervals for true achieved P(CD)

In this paper we present procedures which attempt to allow experimenters to take at least partial advantage of more-favorable configurations of the population parameters (without, in the process, sacrificing precise probability statements about the inferences made) by obtaining confidence intervals for the true probability of a correct decision, regarded as a function of the true unknown underlying parameter values.     

On eliminating inferior regression models

Consider a linear regression model with [p-1] predictor variables which is taken as the "true" model.The goal Is to select a subset of all possible reduced models such that all inferior models ‘to be defined’ are excluded with a guaranteed minimum probability.A procedure is proposed for which the exact evaluation of the probability of a correct decision 1s difficult; however, 1t is shown that the probability requirement can be met for sufficiently large sample size.Monte Carlo evaluation of the constant associated with the procedure and some ways to reduce the amount of computations Involved in the Implementation of the procedure are discussed.     

Distributions of the product and the quotient from bivariates t,f and pareto distribution

This paper deals with the probability density functions of two correlated Pareto, two correlated t and two correlated F random variables.

     

On selecting the treatment with the largest probability of survival

Suppose there are k(>= 2) treatments and each treatment is a Bernoulli process with binomial sampling. The problem of selecting a random-sized subset which contains the treatment with the largest survival probability (reliability or probability of success) is considered. Based on the ideas from both classical approaches and general Bayesian statistical decision approach, a new subset selection procedure is proposed to solve this kind of problem in both balanced and unbalanced designs. Comparing with the classical procedures, the proposed procedure has a significantly smaller selected subset. The optimal properties and performance of it were examined. The methods of selecting and fitting the priors and the results of Monte Carlo simulations on selected important cases are also studied.     

Measuring the degree of severity of heteroskedasticity and the choice between the ols estimator and the 2sae

This paper dwells on the choice between the ordinary least squares and the estimated generalized least squares estimators when the presence of heteroskedasticity is suspected. Since the estimated generalized least squares estimator does not dominate the ordinary least squares estimator completely over the whole parameter space, it is of interest to the researcher to know in advance whether the degree of severity of heteroskedasticity is such that OLS estimator outperforms the estimated generalized least squares (or 2SAE). Casting the problem in the non-spherical error mold and exploiting the principle underlying the Bayesian pretest estimator, an intuitive non-mathematical procedure is proposed to serve as an aid to the researcher in deciding when to use either the ordinary least squares (OLS) or the estimated generalized least squares (2SAE) estimators.     

Department of mathematics university of southampton southampton s09 5nh,england

In this article the screening problem is studied by a predictive approach in a general setting. The problem of optimal screening which is to raise the probability of success after screening to a prespecified value by retaining as many individuals as possible has been solved. The relation between such an optimal screening procedure and that considered in Turkman & Turkman (1989) is illuminated. The bivariate normal model is investigated as an illustration of the general theory.