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，经常会出现涉及相似但独立的调查序列的情况。在这种情况下，当序列以未知的概率分布进行时，感兴趣的参数经常不可预测地变化，因此不能做出通常所称的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。这项研究的部分目的是提出改进的/单调EB估计/检验程序，当响应由某些参数分布建模时，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。

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.