Multivariate Statistcs

该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。它提出承担理论调查，并实际实施，新的统计模型，以应对现代挑战的数据分析。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成群旅行的动物之间的联系。然后，树的分支的随机模型，被认为是线性段的分层集，将被用来表征树的结构，并研究它与其他树的特征（如叶子）的关系。将开发特殊的方法来分析具有数百个捕获场合的大型捕获再捕获数据集，以分析手机上应用程序激活产生的数据集。在调查抽样中，将利用copula模型构建新的小面积估计方法和项目无响应的新归算技术。

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.