Mathematical Sciences: Non Parametric Inference and Sequential Design

该提案的主要目标是研究偏见 投影寻踪中的抽样模型和显著性检验。 对于有偏抽样模型，惩罚最大似然 将寻求估计器，并通过一个 模拟和渐近分析相结合。 技术 从保序估计预计是有用的和新的 技术也将得到发展。 显著性检验 投影寻踪将通过仿真进行研究， 渐近分析，可能借鉴了最近的工作， 高斯随机场的极大值 据证实， 耦合方法可以产生马尔可夫更新定理的证明。 观察性研究经常会遇到或有目的地利用 不等概率抽样模型（称为有偏 抽样模型）。 这项研究的长期目标是 发展推理方法时（不平等） 概率）选择机制。 第二方面 这项研究认为，投影追求，也就是说， 在大型复杂数据集中搜索潜在关系 有很多案例和变量。 特别是，标准 用于确定关系何时被识别 准确地说，将寻求。

The primary objectives of the proposal are to study biased sampling models and tests of significance in projection pursuit. For biased sampling models, penalized maximum likelihood estimators will be sought and their properties analyzed through a combination of simulation and asymptotic analysis. Techniques from isotonic estimation are expected to be useful and new techniques will be developed as well. Significance tests for projection pursuit will be studied through simulation and asymptotic analysis, probably drawing on recent work on the maxima of Gaussian random fields. It is conjectured that coupling methods may yield a proof of the Markov Renewal Theorem. Observational studies often encounter or utilize purposively unequal probability sampling models (referred to as biased sampling models). A long term goal of this research is the development of methodology for inference when the (unequal probability) selection mechanism can be modeled. A second aspect of this research considers projection pursuit, that is, the search for underlying relationships in large complex data sets with many cases and with many variables. In particular, criteria for determining when relationships have been recognized accurately will be sought.