Monotone empirical bayes, non/semiparametric methods for nonlinear/hazards/censored regression and functional estimation

在许多领域，如医学、农业、工业、工程、生物科学、社会学，经常出现涉及类似但独立的调查序列的情况。在这种情况下，随着序列的发展，感兴趣的参数通常会随着未知的概率分布而发生不可预测的变化，因此无法做出最小风险决策，即通常所说的贝叶斯决策。然而，从以前的调查中收集的信息有时可以用来制定决策，即通常所说的经验贝叶斯决策，其风险接近最小贝叶斯风险。本研究的部分目的是在响应由某些参数分布建模时提出改进的/单调EB估计/测试程序，并调查这些程序的风险接近最小贝叶斯风险的速度和最佳可能速度。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。本研究计划的部分目标是开发改进的非/半参数回归模型，用于审查样本的协变量效应，并研究效率和最佳收敛率。在几乎每个学科中，响应数据都依赖于几个因果协变量，人们经常面临基于这些协变量对响应数据进行建模以进行预测/预测的问题。这项研究计划部分是为了扩展预测/预测的方法，而不需要对协变量的响应的依赖（回归）的功能形式进行任何说明，其中这些变量可能是随机的（或时间）依赖于经济学，也可能是生命周期数据，如生存分析。

In many fields, like medicine, agriculture, industry, engineering, biological sciences, sociology, often situations involving sequences of similar but independent investigations arise. In such situations the parameter of interest often varies unpredictably as the sequence progresses with unknown probability distribution, and hence a minimum risk decision, what is usually called Baysian decision, can not be made. However, the information collected from the previous investigations can sometimes be utilized to formulate a decision, what is popularly known as empirical Bayes decision, with risk close to the minimum Bayes risk. Part of the objective of this research is to propose improved/monotone EB estimation/test procedures when the responses are modelled by some parametric distribution and to investigate the speed and the best possible speed with which the risk of these procedures approach to the minimum Bayes risk.  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.  Part of the objective of this research proposal is to develop improved non/semi-parametric regression models for covariate effects with censored samples and to investigate the efficiency and the optimal convergence rates.In almost every discipline response data depend on several causal co-variates, and one is often faced with the problem of modelling the response data on these co-variates for forecasting/prediction purpose. This research proposal is in part to extend the methods of forecasting/prediction  without any specification of the functional form of the dependence (regression) of the responses on covariates, where these variables may be stochastically  (or time) dependent as in economics or may be life time data as in survival analysis.