Mathematical Sciences: Non Parametric Inference and Sequential Design

该提案的主要目标是研究有偏抽样模型和投影寻踪中的重要性检验。对于有偏抽样模型，将通过模拟和渐近分析相结合的方法来寻找惩罚最大似然估计，并分析其性质。预计等张估计技术将是有用的，新技术也将被开发。投影寻踪的显著性检验将通过模拟和渐近分析来研究，可能借鉴最近关于高斯随机场极大值的工作。推测耦合方法可以给出马尔可夫更新定理的一个证明。观察性研究经常遇到或利用故意的不等概率抽样模型(称为有偏抽样模型)。这项研究的一个长期目标是发展当(不等概率)选择机制可以被建模时的推理方法。这项研究的第二个方面考虑了投影寻踪，即在具有多个情况和多个变量的大型复杂数据集中寻找潜在关系。特别是，将寻求确定关系何时被准确识别的标准。

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.