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

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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.**** 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 modeled 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.**** In almost every discipline a response depends on several causal covariates, (e.g., carbohydrate in an insulin dependent diabetic male depends on his age, weight, protein etc.) and one is often faced with the problem of modeling the response data on the covariates for forecasting and prediction purpose. Part of the objectives of this research proposal is to extend the research on forecasting/prediction problem to the situations where we deal simultaneously with two or more systems of models where responses depend on two or more sets of covariates. We utilize all the information on covariates to fit models to provide the best prediction/forecasting procedures. This technique, what is originally known in economics, as the system of seemingly unrelated regressions, is becoming more and more popular in other disciplines such as social and biological sciences, epidemiology, geography, engineering and reliability. In some situations where such system occurs independently, we plan to apply empirical Bayes method to obtain better procedures.************