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

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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.