Mathematical Sciences: Studies in Nonparametric and Semiparametric Statistics

该研究涉及截尾数据存在下的半参数和非参数统计模型的研究。将开发图形模型诊断方法，以比较两个样本实验中两组的风险经验，并对COX回归模型进行拟合优度检验。将开发非参数回归的置信度范围程序，并将在风险函数估计的带宽选择问题中给出基于数据的规则。响应变量和预测变量之间的关系将通过半参数速率函数和转换模型来研究。还将考虑采用程序来测试配对生存时间的独立性。

The research involves the study of semiparametric and nonparametric statistical models in the presence of censored data. Graphical model diagnostic methods will be developed to compare the hazard experience of two groups in two-sample experiments and for goodness-of-fit tests of the Cox regression model. Confidence band procedures will be developed for nonparametric regression and data-based rules will be given in bandwidth selection problems for hazard function estimation. The relationships between the response variable and predictor variables will be studied through semparametric rate functions and transformation models. Procedures will also be considered for testing independence of paired survival times.