On construction of the smallest one-sided confidence interval for the difference of two proportions

For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at level $\alpha$ is obtained. A generalization of constructing the smallest one-sided confidence interval to other discrete sample spaces is discussed in the presence of nuisance parameters.Comment: Published in at http://dx.doi.org/10.1214/09-AOS744 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Step-up simultaneous tests for identifying active effects in orthogonal saturated designs

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given $\alpha$ level in the strong sense.Comment: Published at http://dx.doi.org/10.1214/009053606000001136 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Isomorphic routing on a toroidal mesh

We study a routing problem that arises on SIMD parallel architectures whose communication network forms a toroidal mesh. We assume there exists a set of k message descriptors (xi, yi), where (xi, yi) indicates that the ith message's recipient is offset from its sender by xi hops in one mesh dimension, and yi hops in the other. Every processor has k messages to send, and all processors use the same set of message routing descriptors. The SIMD constraint implies that at any routing step, every processor is actively routing messages with the same descriptors as any other processor. We call this isomorphic routing. Our objective is to find the isomorphic routing schedule with least makespan. We consider a number of variations on the problem, yielding complexity results from O(k) to NP-complete. Most of our results follow after we transform the problem into a scheduling problem, where it is related to other well-known scheduling problems

A Unified Approach for Constructing Confidence Intervals and Hypothesis Tests Using h-function

We introduce a general method, named the h-function method, to unify the con- structions of level- exact test and 1− exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate interval, including a point estimator, is modified to an exact interval; ii) an exact interval is refined to be an interval that is a subset of the previous one. Two real datasets are used to illustrate the method

Extended Quark Potential Model from Random Phase Approximation

The quark potential model is extended to include the sea quark excitation using the random phase approximation (RPA). The effective quark interaction preserves the important Quantum Chromodynamics (QCD) properties -- chiral symmetry and confinement simultaneously. A primary qualitive analysis shows that the $\pi$ meson as a well-known typical Goldstone boson and the other mesons made up of valence $q\bar{q}$ quark pair such as the $\rho$ meson can also be described in this extended quark potential model

Modelling of airflow and aerosol particle movement in buildings.

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