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Ashish Das Aloke Dey Ling-Yau Chan Kashinath Chatterjee 《Journal of statistical planning and inference》2008
A popular measure to assess 2-level supersaturated designs is the E(s2) criterion. In this paper, improved lower bounds on E(s2) are obtained. The same improvement has recently been established by Ryan and Bulutoglu [2007. E(s2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. However, our analysis provides more details on precisely when an improvement is possible, which is lacking in Ryan and Bulutoglu [2007. E(s2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. The equivalence of the bounds obtained by Butler et al. [2001. A general method of constructing E(s2)-optimal supersaturated designs. J. Roy. Statist. Soc. B 63, 621–632] (in the cases where their result applies) and those obtained by Bulutoglu and Cheng [2004. Construction of E(s2)-optimal supersaturated designs. Ann. Statist. 32, 1662–1678] is established. We also give two simple methods of constructing E(s2)-optimal designs. 相似文献
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Joseph P.S. Kung Anna de Mier Xinyu Sun Catherine Yan 《Journal of statistical planning and inference》2009
We consider paths in the plane with (1,0), (0,1), and (a,b)-steps that start at the origin, end at height n, and stay strictly to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at most b/a, then the ordinary generating function for the number of such paths ending at height n is algebraic. Our argument is in two parts. We use a simple combinatorial decomposition to obtain an Appell relation or “umbral” generating function, in which the power zn is replaced by a power series of the form znφn(z), where φn(0)=1. Then we convert (in an explicit way) the umbral generating function to an ordinary generating function by solving a system of linear equations and a polynomial equation. This conversion implies that the ordinary generating function is algebraic. We give several concrete examples, including an alternative way to solve the tennis ball problem. 相似文献