Showing papers by "Rahul Mukerjee published in 2006"

A modern theory of factorial designs

Abstract: The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. This book gives, for the first time in book form, a comprehensive and up-to-date account of this modern theory. Many major classes of designs are covered in the book. While maintaining a high level of mathematical rigor, it also provides extensive design tables for research and practical purposes. Apart from being useful to researchers and practitioners, the book can form the core of a graduate level course in experimental design.

Empirical-type likelihoods allowing posterior credible sets with frequentist validity: Higher-order asymptotics

Abstract: SUMMARY With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest posterior density. These asymptotics, in turn, characterise members of the class that allow approximate frequentist validity of such sets. It is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here.

D-optimal designs for covariate models

Abstract: The problem of finding D-optimal or D-efficient designs in the presence of covariates is considered under a completely randomized design set-up with v treatments, k covariates and N experimental units. In contrast to Lopes Troya [Lopes Troya, J., 1982, Optimal designs for covariates models. Journal of Statistical Planning and Inference, 6, 373–419.], who considered this problem in the equireplicate case, we do not assume that N/v is an integer, and this allows us to study situations where no equireplicate design exists. Even when N/v is an integer, it is seen quite counter-intuitively that there are situations where a non-equireplicate design outperforms the best equireplicate design under the D-criterion.

Optimal (2, n) visual cryptographic schemes

Abstract: In (2,n) visual cryptographic schemes, a secret image(text or picture) is encrypted into n shares, which are distributed among n participants. The image cannot be decoded from any single share but any two participants can together decode it visually, without using any complex decoding mechanism. In this paper, we introduce three meaningful optimality criteria for evaluating different schemes and show that some classes of combinatorial designs, such as BIB designs, PBIB designs and regular graph designs, can yield a large number of black and white (2,n) schemes that are optimal with respect to all these criteria. For a practically useful range of n, we also obtain optimal schemes with the smallest possible pixel expansion.

Asymptotic results on a general class of empirical statistics: power and confidence interval properties

Abstract: We consider a very general class of empirical statistics that includes (a) empirical discrepancy (ED) statistics, (b) generalized empirical exponential family likelihood statistics, (c) generalized empirical likelihood statistics, (d) empirical statistics arising from Bayesian considerations, and (e) Bartlett-type adjusted versions of ED statistics. With reference to this general class, we investigate higher order asymptotics on power and expected lengths of confidence intervals. For (b)-(e), such results have been hitherto unexplored. Furthermore, our findings help in understanding the presently known results on the subclass (a) from a wider perspective.