Mathematical Sciences: Topics in Statistical Theory

研究项目涉及统计重抽样方法、定向数据分析、生存分析和半参数模型。将支持制定涵盖自助法和折叠法的重新抽样程序的统一理论。从来自平稳m相依随机变量序列的k个采样块得到的元素将被用于提供参数的自举估计器，并且将检查估计器的属性。将调查这些重采样程序的稳健性问题。方向性数据的数据深度的概念将与它们的非参数检验和相应的数据分类一起发展。对于截尾数据和非截尾数据，将研究用于生存分析的半参数模型。

The research project involves statistical resampling methods, analysis of directional data, survival analysis and semiparametric models. The development of a unified theory of resampling procedures that covers both the bootstrap and the jackknife methods will be supported. The resulting elements from k sampled blocks from a sequence of stationary m-dependent random variables will be used to provide bootstrap estimators of parameters and the properties of the estimators will be examined. Questions of robustness of these resampling procedures will be investigated. Notions of data depth for directional data will be developed along with nonparametric tests for them and corresponding classifications of data. Semiparametric models for survival analysis will be be studied for both censored and non- censored data.