Rahul Mukerjee

Randomized response : theory and techniques

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Fractional factorial plans

Fractional Plans and Orthogonal Arrays. Symmetric Orthogonal Arrays. Asymmetric Orthogonal Arrays. Some Results on Nonexistence. More on Optimal Fractional Plans and Related Topics. Trend-Free Plans and Blocking. Some Further Developments. Appendix. References. Index.

Probability matching priors : higher order asymptotics

Introduction and the Shrinkage Argument.- Matching Priors for Posterior Quantiles.- Matching Priors for Distribution Functions.- Matching Priors for Highest Posterior Density Regions.- Matching Priors for Other Credible Regions.- Matching Priors for Prediction.

Uniformity in Fractional Factorials

The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two- or three-level factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching for minimum aberration designs.

Some new Results on Probability Matching Priors

The paper has three components. First, for a realvalued parameter of interest orthogonal (Cox and Reid, 1987) to the nuisance parameter vector, we find a necessary and sufficient condition for the equivalence of second order quantile matching priors and highest posterior density regions matching priors within the class of first order quantile matching priors. Examples are presented to illustrate the result. Second, we develop a quantile matching prior in a normal hierarchical Bayesian model. This prior turns out to be different from the one proposed earlier by Morris (1983). Third, we obtain an exact matching result when the objective is prediction of a real-valued random variable from a location family of distributions. AMS (2000) Subject Classification: 62F15, 62F25, 62E20

Optimal repeated measurements designs under interaction

The robustness of some optimality results on repeated measurements designs is investigated when the underlying model is allowed to be non-additive incorporating an interaction due to the direct and residual effects of treatments. The procedure involves the checking of some orthogonality conditions and the calculus for factorial arrangements is applied for this purpose. Some new constructions of optimal repeated measurements designs have also been considered.

Optimal (k, n) visual cryptographic schemes for general k

In (k, n) visual cryptographic schemes (VCS), a secret image is encrypted into n pages of cipher text, each printed on a transparency sheet, which are distributed among n participants. The image can be visually decoded if any k(≥2) of these sheets are stacked on top of one another, while this is not possible by stacking any k − 1 or fewer sheets. We employ a Kronecker algebra to obtain necessary and sufficient conditions for the existence of a (k, n) VCS with a prior specification of relative contrasts that quantify the clarity of the recovered image. The connection of these conditions with an L1-norm formulation as well as a convenient linear programming formulation is explored. These are employed to settle certain conjectures on contrast optimal VCS for the cases k = 4 and 5. Furthermore, for k = 3, we show how block designs can be used to construct VCS which achieve optimality with respect to the average and minimum relative contrasts but require much smaller pixel expansions than the existing ones.

Bartlett-type modification for Rao's efficient score statistic

This paper suggests simple Bartlett-type modifications for a wide class of test statistics that includes in particular the efficient score and the likelihood ratio statistics.

Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics

We explore two proposals for finding empirical Bayes prediction intervals under a normal regression model. The coverage probabilities and expected lengths of such intervals are studied and compared via appropriate higher-order asymptotics.

Comparison of Bartlett-type adjustments for the efficient score statistic

Several Bartlett-type adjustments for the efficient score statistic have been recently proposed in the literature. This article compares them, under contiguous alternatives, with reference to the criteria of maximinity and average power.