Showing papers by "Rahul Mukerjee published in 2017"
TL;DR: In this paper, the authors derived central limit theorems for four types of U-designs by introducing a newly constructed discrete function and showed that the means of the four samples generated from these four types asymptotically follow the same normal distribution.
Abstract: Orthogonal array (OA)-based Latin hypercube designs, also called U-designs, have been popularly adopted in designing a computer experiment. Nested U-designs, sliced U-designs, strong OA-based U-designs and correlation controlled U-designs are four types of extensions of U-designs for different applications in computer experiments. Their elaborate multi-layer structure or multi-dimensional uniformity, which makes them desirable for different applications, brings difficulty in analysing the related statistical properties. In this paper, we derive central limit theorems for these four types of designs by introducing a newly constructed discrete function. It is shown that the means of the four samples generated from these four types of designs asymptotically follow the same normal distribution. These results are useful in assessing the confidence intervals of the gross mean. Two examples are presented to illustrate the closeness of the simulated density plots to the corresponding normal distributions.
3 citations
TL;DR: In this article, the A-optimal block designs in small blocks are explored under the A-, E- and D-criteria when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments.
Abstract: Optimal block designs in small blocks are explored under the A-, E- and D-criteria when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first formulate the problem via approximate theory which leads to a convenient multiplicative algorithm for obtaining A-optimal design measures. This, in turn, yields highly efficient exact designs, under the A-criterion, 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 in possibly several stages. Illustrative examples are given and tables of A-optimal design measures are provided. Approximate theory is also seen to yield analytical results on E- and D-optimal design measures.