Multivariate Statistcs

这项研究项目涉及统计科学的几个领域，即几何统计、捕获-再捕获实验、调查抽样和Copula建模。它建议进行新的统计模型的理论研究和实际实施，以应对数据分析方面的现代挑战。首先将开发随机效应循环回归模型，其动机是需要量化生态学中群体旅行的动物之间的关联。然后，树的树枝的随机模型，被认为是一组分层的线性段，将被用来描述树的结构，并调查它如何与其他树的特征相关联，例如它的叶子。将开发特殊方法来分析具有数百次捕获时机的大型捕获重新捕获数据集，以分析手机上激活应用程序所生成的数据集。在调查抽样中，将使用Copula模型来构造新的小区域估计方法和项目无响应的新的估计技术。

This research project is concerned with several areas of the statistical sciences, namely geometric statistics, capture-recapture experiments, survey sampling and copula modeling. It proposes to undertake the theoretical investigations, and the practical implementation, of new statistical models in response to modern challenges in data analysis. First random effects circular regression models will be developed, motivated by the need to quantify the association between animals traveling in groups in ecology. Then stochastics models for the branches of a tree, considered as a hierarchical set of linear segments, will be used to characterize the structure of a tree and to investigate how it is related to other tree’s characteristics, such as its foliage. Special methods to analyze large capture recapture data sets featuring hundreds of capture occasions will be developed, to analyze data sets generated by the activation of applications on mobile phones. In survey sampling, copula models will be used to construct new small area estimation methods and new techniques of imputation for item non response.