Design of Experiments and Canonical Moments

本研究由两个相关的部分组成：一部分是实验设计，另一部分是统计学和概率论中的正则矩。设计领域的研究涉及复杂计算机代码的分析，回归理论中有理函数的使用以及刚性设计的分析。复杂的计算机代码被渐近地分析，以便最优地选择输入值用于进一步的预测目的。该理论涉及随机过程、多维插值理论和近似理论的使用。第二部分涉及到实线上分布的归一化矩的使用，称为正则矩。这些方法已成功地应用于一维多项式回归的实验设计。本研究探讨了矩理论和随机漫步中一些尚未解决的问题。实验设计问题通常涉及如何选择进行哪些实验，以最小的成本获得最大的信息。目前的研究涉及对复杂计算机代码的分析，其中的问题是确定最佳输入值以预测其他可能输入值的结果。这与高性能计算密切相关，高性能计算是NSF当前的战略领域之一。

DMS 9626784 Studden This research is composed of two related parts: one part deals with the design of experiments and the other deals with canonical moments in Statistics and Probability. The research in the design area involves the analysis of complex computer codes, the use of rational functions in regression theory and the analysis of rigid designs. Complex computer codes are analysed asympotically in order to optimally choose input values to use for further prediction purposes. The theory involves the use of stochastic processes, multidimensional interpolation theory and approximation theory. The second part involves the use of normalized moments of distributions on the real line called canonical moments. These have been used successfully in designing experiments in one dimensional polynomial regression. The present study investigates some unanswered questions in moment theory and random walks. Experimental design problems in general involve how to choose which experiments to conduct to obtain maximal information at minimal cost.The present research involves the analysis of complex computer codes where the problem is to decide on optimal input values to predict the outcome at other possible input values. This relates significantly to high performance computing which is one of NSF's current strategic areas.