Mathematical Sciences: Non Parametric Inference and Sequential Design

本文的主要目的是研究投影寻踪中的偏差抽样模型和显著性检验。对于有偏抽样模型，将寻求惩罚最大似然估计量，并通过模拟和渐近分析相结合来分析其性质。等压估计技术有望发挥作用，新技术也将得到发展。投影追踪的显著性检验将通过模拟和渐近分析来研究，可能会借鉴最近关于高斯随机场最大值的工作。本文推测耦合方法可以得到马尔可夫更新定理的一个证明。观察性研究经常遇到或有意利用不等概率抽样模型（称为有偏抽样模型）。本研究的长期目标是在（不等概率）选择机制可以建模的情况下发展推理方法。本研究的第二个方面考虑了投影追踪，即在具有许多情况和许多变量的大型复杂数据集中寻找潜在关系。特别是，将寻求确定何时准确识别关系的标准。

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.