Mathematical Sciences: Topics in Statistical Theory

该研究项目涉及统计重采样方法、定向数据分析、生存分析和半参数模型。将支持重新采样过程的统一理论的发展，该理论涵盖了自举法和折刀法。从平稳的m相关随机变量序列的k个采样块中得到的结果元素将用于提供参数的自举估计器，并且将检查估计器的性质。这些重采样程序的鲁棒性问题将被调查。定向数据的数据深度概念将随着定向数据的非参数检验和相应的数据分类而发展。半参数模型的生存分析将被研究为审查和非审查的数据。

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.