Bayesian robustness for multiparameter problems

Bayesian robustness is studied for ε-contamination classes of prior distributions. Nonparametric classes of contsminations such as the class of all unimodal spherically symmetric densities are considered here. Posterior φ-divergence and its curvature are used to measure the sensitivity of priors on the resulting posterior densities. Examples are provided to illustrate our results.     

Estimation of scale parameters in mixture distributions

Simultaneous estimation of scale parameters is considered in mixture distributions under squared-error loss. A general class of estimators is obtained which dominates the componentwise best multiple estimators and the moment estimators. As special cases, improved estimators are obtained for the multivariate t-distribution and the p-variate Lomax distribution.     

Bayesian approach to estimation of intraclass correlation using reference prior

For the balanced variance component model when the intraclass correlation coefficient is of interest, Bayesian analysis is often appropriate. Berger and Bernardo’s (1992a) grouped ordering reference prior approach is used to analyze this model. The reference priors are developed and compared for the posterior inference with real and simulated data. We examine whether the reference priors satisfy the probability-matching criterion. Further, the reference prior is shown to be good in the sense of correct frequentist coverage probability of the posterior quantile.     

Retail competition in the fast-moving consumer goods industry: The case of France and the UK

UK retailers in the fast-moving consumer goods industry focus their strategy on building loyalty through quality ‘own’ labels. By contrast, French retailers compete aggressively on price. Judy and Marcel Corstjens, and Rajiv Lal argue that either a ‘two-tier’ or parallel system will evolve in the future or a national industry will tend to oscillate from one strategy to another. Retailers must decide which of the two strategies they will consistently adopt.     

On Some Chemical Balance Weighing Designs

The present paper deals with certain chemical balance weighing designs. The incidence matrices of BIB designs and balanced ternary designs have been used to construct these designs. Conditions have been obtained to make some of these designs “optimum”.     

Comparison of two sampling schemes for generating record-breaking data from the proportional hazard rate models

ABSTRACT

In this article, we consider a sampling scheme in record-breaking data set-up, as record ranked set sampling. We compare the proposed sampling with the well-known sampling scheme in record values known as inverse sampling scheme when the underlying distribution follows the proportional hazard rate model. Various point estimators are obtained in each sampling schemes and compared with respect to mean squared error and Pitman measure of closeness criteria. It is observed in most of the situations that the new sampling scheme provides more efficient estimators than their counterparts. Finally, one data set has been analyzed for illustrative purposes.     

On the choice of co-ordinates in simultaneous estimation of normal means under misspecification of normal priors

The problem of choice of coordinates in Stein-type estimators,when simultaneously estimating normal means, is considered. The question of deciding whether to use all coordinates in one combined shrinkage estimators or to separate into groups and use separate shrinkage estimators on each group is considered in the situation in which part of the prior information may be " misspecified". It is observed that the amount of misspecification determines whether to use the combined shrinkage estimator the separate shrinkage estimator.     

Estimation of parameters and reliability from generalized life models

Simultaneous estimation of parameters with p (≥ 2) components, where each component has a generalized life distribution, is considered under a sum of squared error loss function. Improved estimators are obtained which dominate the maximum likelihood and the niinimum mean square estimators. Robustness of the improved estimators is shown even when the component distributions are dependent. The result is extended to the estimation of the system reliability when the components are connected in series. Several numerical studies are performed to demonstrate the risk improvement and the Pitman closeness of the new estimators.     

Discriminating between the Weibull and log-normal distributions for Type-II censored data

Log-normal and Weibull distributions are the two most popular distributions for analysing lifetime data. In this paper, we consider the problem of discriminating between the two distribution functions. It is assumed that the data are coming either from log-normal or Weibull distributions and that they are Type-II censored. We use the difference of the maximized log-likelihood functions, in discriminating between the two distribution functions. We obtain the asymptotic distribution of the discrimination statistic. It is used to determine the probability of correct selection in this discrimination process. We perform some simulation studies to observe how the asymptotic results work for different sample sizes and for different censoring proportions. It is observed that the asymptotic results work quite well even for small sizes if the censoring proportions are not very low. We further suggest a modified discrimination procedure. Two real data sets are analysed for illustrative purposes.