Showing papers by "Rahul Mukerjee published in 2014"
TL;DR: This work develops a method for construction of arrays which are nearly Orthogonal, in the sense that each column is orthogonal to a large proportion of the other columns, and which are convertible to fully orthogonic arrays via a mapping of the symbols in each column to a possibly smaller set of symbols.
Abstract: We develop a method for construction of arrays which are nearly orthogonal, in the sense that each column is orthogonal to a large proportion of the other columns, and which are convertible to fully orthogonal arrays via a mapping of the symbols in each column to a possibly smaller set of symbols. These arrays can be useful in computer experiments as designs which accommodate a large number of factors and enjoy attractive space-filling properties. Our construction allows both the mappable nearly orthogonal array and the consequent fully orthogonal array to be either symmetric or asymmetric. Resolvable orthogonal arrays play a key role in the construction.
14 citations
TL;DR: In this article, the authors derive asymptotic results leading to explicit formulae for two-sided Bayesian and frequentist tolerance intervals and derive probability matching priors for such intervals.
Abstract: It is well known that that the construction of two-sided tolerance intervals is far more challenging than that of their one-sided counterparts. In a general framework of parametric models, we derive asymptotic results leading to explicit formulae for two-sided Bayesian and frequentist tolerance intervals. In the process, probability matching priors for such intervals are characterized and their role in finding frequentist tolerance intervals via a Bayesian route is indicated. Furthermore, in situations where matching priors are hard to obtain, we develop purely frequentist tolerance intervals as well. The findings are applied to real data. Simulation studies are seen to lend support to the asymptotic results in finite samples.
4 citations
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TL;DR: In this article, the robustness of fractional factorial models to model misspecification is investigated using a minimaxity approach, which works well even when the run size is quite small.
Abstract: With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully devised discretization procedures. The robustness of these designs to possible model misspecification is investigated using a minimaxity approach. Examples are given to demonstrate that our technique works well even when the run size is quite small.
3 citations
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TL;DR: In this article, the optimal design problem under second-order least squares estimation was studied, and a general approximate theory was developed, taking cognizance of the nonlinearity of the underlying information matrix in the design measure.
Abstract: We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed, taking due cognizance of the nonlinearity of the underlying information matrix in the design measure. This yields necessary and sufficient conditions that a D- or A-optimal design measure must satisfy. The results are then applied to find optimal design measures when the design points are binary. The issue of reducing the support size of the optimal design measure is also addressed.
1 citations
TL;DR: In this paper, the authors proposed a new unequal probability scheme for shared key operations, which improves upon the values of anonymity measures, as quantified via appropriate conditional probabilities, over the existing ones, which are based on equal probability selection.
Abstract: We propose a new unequal probability scheme for shared key operations. It is seen that this scheme improves upon the values of anonymity measures, as quantified via appropriate conditional probabilities, over the existing ones, which are based on equal probability selection.
1 citations
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TL;DR: In this article, the optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments, and an approximate theory is developed which leads to a convenient multiplicative algorithm for obtaining optimal design measures.
Abstract: Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative algorithm for obtaining optimal design measures. This, in turn, yields highly efficient exact designs even when the number of blocks is rather small. Moreover, our approach is seen to allow nesting of such efficient exact designs which is an advantage when the resources for the experiment are available possibly in several stages. Illustrative examples are given. Tables of optimal design measures are also provided.