Mathematical Sciences: "Nonlinear Modeling of Spatially Correlated Data: Preliminary Investigations"

Jacqueline M.Hughes-Oliver North Carolina State University在半导体行业的数据收集是这样的：重复测量-通过单个晶片上的空间网格获得-是正常的，而不是例外。在这个拟议的规划期之后，计划的研究目标是发展具有非平稳、非正态误差的空间相关数据的非线性建模的方法学进展。这项工作受到两个现实生活应用程序的很好激励，这两个应用程序都表明了对这些进步的迫切需求。对重复测量的分析研究的一个主要结果是发现，如果实验单元的数量远远超过重复测量的数量，则不需要仔细地表示关联结构。然而，半导体行业的晶圆成本限制了对非常多晶圆的数据收集。因此，必须仔细地表示可能的非平稳误差协方差结构。这是规划活动的第一步。还必须根据(新的)相关结构研究具体的建模和估计技术。这些构成了额外的规划活动。要对这些半导体工艺进行现实建模，需要放松正态假设，并愿意考虑非线性模型。规划活动包括对这些概括性问题引起的复杂情况进行初步调查。最后一项活动是制定国家科学基金会的常规提案。

Jacqueline M. Hughes-Oliver North Carolina State University Data collection in the semiconductor industry is such that repeated measurements --- obtained over a spatial grid on a single wafer --- are the norm, not the exception. Following this proposed planning period, the projected research goal is the development of methodological advances for nonlinear modeling of spatially correlated data with nonstationary, nonnormal errors. This work is well motivated by two real-life applications, which both indicate immediate need for these advances. A major result of research on the analysis of repeated measurements is the discovery that careful representation of the correlation structure is not necessary, provided the number of experimental units far exceeds the number of repeated measurements. The cost of wafers in the semiconductor industry, however, prohibits collection of data for very many wafers. Hence, careful representation of the possibly nonstationary error covariance structure must be undertaken. This constitutes the first of the planning activities. Specific modeling and estimation techniques must also be investigated in light of the (new) correlation structures. These constitute additional planning activities. Realistic modeling of these semiconductor processes require relaxing the assumption of normality, and a willingness to consider nonlinear models. Planning activities include preliminary investigations of the complications arising from these generalities. The final activity is the development of the regular NSF proposal.