Non/semiparametric methods for nonlinear/hazards/cencored regression; Nonparametric monotone empirical Bayes; Non/semiparametric seemingly unrelated regression

当响应是时间到事件的结果时，例如患者的寿命，失败时间，数据通常被审查并涉及时间相关协变量。例如，在一项临床试验中，研究人员感兴趣的是评估一种治疗对HIV-1血清阳性吸毒者生存的影响，这些吸毒者调整了其他预测性协变量，如身体质量指数（BMI）和年龄。当研究结束时，一些患者可能还活着。因此，这些患者的生存时间被删减。另一方面，当患者来自不同的医疗中心时，同一中心的患者之间可能存在依赖关系。本研究计划的部分目标是开发改进的非/半参数回归模型，用于固定和混合协变量效应与截尾和聚类样本，并研究估计器的大样本性能以及它们的效率和最佳收敛率。

When the response is the time-to-event outcome such as lifetimes of patients, failure times, the data are often censored and involve time dependent covariates. For example, in a clinical trial, the researchers are interested in evaluating the effect of a treatment on survival in the HIV-1 seropositive drug users adjusted for other predictive covariates such as BMI (body mess index) and age. Some patients may still be alive when the study terminates. Hence, the survival time of these patients are censored. On the other hand, when patients are taken from different health centers, there might be a dependence between patients in the same centers. Part of the objective of this research proposal is to develop improved non/semi-parametric regression models for fixed and mixed covariate effects with censored and clustered samples and to investigate the large sample performance of the estimators as well as their efficiency and the optimal convergence rates.