Mathematical Sciences: Topics in Statistical Theory

这个研究项目涉及到统计调查 方法、定向数据分析、生存分析和 半参数模型发展一个统一的理论， 重新启动过程，该过程涵盖引导程序和 将支持折刀方法。由以下元素生成的元素 k个采样块从一个平稳的m-依赖随机序列 变量将用于提供以下各项的自助估计值： 参数和估计的属性将被检查。 这些重新部署程序的稳健性问题将是 研究了定向数据的数据深度概念如下： 沿着非参数检验， 数据的相应分类。半参数模型 将研究删失和非删失的生存分析 删失数据

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.