Showing papers by "Rahul Mukerjee published in 1995"

On the existence of saturated and nearly saturated asymmetrical orthogonal arrays

Abstract: We develop a combinatorial condition necessary for the existence of a saturated asymmetrical orthogonal array of strength 2. This condition limits the choice of integral solutions to the system of equations in the Bose-Bush approach and can thus strengthen considerably the Bose-Bush approach as applied to a symmetrical part of such an array. As a consequence, several nonexistence results follow for saturated and nearly saturated orthogonal arrays of strength 2. One of these leads to a partial settlement of an issue left open in a paper by Wu, Zhang and Wang. Nonexistence of a class of saturated asymmetrical orthogonal arrays of strength 4 is briefly discussed.

Frequentist validity of highest posterior density regions in the presence of nuisance parameters

Abstract: Priors ensuring frequentist validity, up to o(n ), of credible regions based on the highest posterior density have been characterized in the presence of nuisance parameters. In this connection, the consequences of an orthogonal parametrization have also been discussed. 1: Introduction In recent years, there has been a revival of interest in problems relating to approximate frequentist validity of posterior credible regions. As noted in Tibshirani (1989), apart from providing a method for constructing accurate frequentist confidence regions, such studies are also helpful in defining noninformative priors which could be potentially useful for comparative purposes in a Bayesian analysis. The results available in the literature in this general area include those related to the approximate frequentist validity of one-sided posterior regions based on posterior quantiles ([18], [13], [16], [17], [12]), posterior regions based on the inversion of likelihood ratio and related statistics ([7], [8]) and highest posterior density (HPD) regions ([14], [9]). We refer to [11] and [15] for further interesting results and references. As for the problem of characterizing priors ensuring approximate frequentist validity of HPD regions, it appears that not much work has as yet been done on models involving nuisance parameters. In consideration of the current interest on such models, in this work we propose to fill up this gap to some extent. As a special case, models with an orthogonal parametrization ([5]) have been considered. An advantage of our approach is that it does not require an explicit evaluation of all the coefficients involved in the (approximate) posterior density of the interest parameter and this keeps the algebra relatively simple (see Section 3). AMS subject classification: 62F15, 62F25, 62E20 Key word· and phrases: highest posterior density, non-informative prior, parametric orthogonality.

On posterior credible sets based on score statistic

Abstract: Conditions for approximate frequentist validity of posterior credible sets based on the score statistic have been derived in the multiparameter case. These conditions can be helpful in supplementing similar conditions obtainable through the likelihood ratio statistic and the highest posterior density region. In the process, explicit expressions are given for the posterior quantiles of the score statistic. Similar results based on Wald's statistic have also been briefly indicated.

On Perturbed Ellipsoidal and Highest Posterior Density Regions with Approximate Frequentist Validity

Abstract: This paper considers, in the multiparameter case, perturbed ellipsoidal and highest posterior density regions with both Bayesian and frequentist validity up to o(n -1 ).

On Perturbed Ellipsoidal and Highest Posterior Density Regions with

Abstract: SUMMARY This paper considers, in the multiparameter case, perturbed ellipsoidal and highest posterior density regions with both Bayesian and frequentist validity up to o (n-I).