Mathematical Sciences: Topics in Semiparametric Inference, with Special Reference to Survival Analysis

将对半参数推断中的问题进行统计研究，大多数问题与生存分析有关，少数问题具有序贯性质。在两样本加速寿命模型中，基于截尾生存分析数据，对相对尺度参数进行序贯检验。该模型是半参数的，因为相对比例参数是参数分量，而基线分布是非参数分量。将为这一问题开发连续有效分数测试，作为连续LOGRANK测试的替代方案。我们还将分析这方面的更一般版本。在带有删失数据的加速寿命模型中，估计也将被研究。这些设置将包括对生存数据的序贯临床试验中经过的时间的研究，对脆弱导致的双变量模型的推断，对比例平均剩余寿命模型的推断，半参数模型中的加权U-统计量，大样本的“完整性”，以及蒙特卡罗检验的序贯停止规则。

Statistical research on problems in semiparametric inference will be conducted with most relating to survival analysis and several with a sequential nature. Sequential tests will be constructed for the relative-scale parameter based on survival analysis data with censoring in a two-sample accelerated-life model. The model is semiparametric in that the relative scale parameter is a parametric component while the baseline distribution is a nonparametric component. Sequential effective score tests will be developed for this problem as an alternative to sequential logrank tests. More general versions of this will also be analyzed. Estimation will also be studied in accelerated- life models with censored data. The settings will include the study of elapsed time in sequential clinical trials on survival data, inference for bivariate models induced by frailties, inference for proportional-mean-residual-life models, weighted U- statistics in semiparametric models, large-sample "completeness", and sequential stopping rules for Monte Carlo tests.