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、工程学、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，感兴趣的参数往往会随着序列以未知的概率分布前进而不可预测地变化，因此不能做出通常称为贝叶斯决策的最小风险决策。然而，从以前的调查中收集的信息有时可以用来制定一个决策，通常称为经验贝叶斯决策，风险接近最小贝叶斯风险。本研究的部分目的是提出改进的/单调EB估计/测试程序时，响应建模的一些参数分布和调查的速度和最好的速度，这些程序的风险接近最小贝叶斯风险。

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.