Non/semiparametric methods for nonlinear/hazards/censored 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, data are often clustered and censored. For example, in a clinical trial, 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 times 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 center. Part of the objective of this research proposal is to develop 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. In many fields, like medicine, industry, engineering and biological sciences, 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, cannot 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 procedures with risks close to the minimum Bayes risk. In almost every discipline a response data depend on several causal covariates, and one is often faced with the problem of modeling the response data on covariates for forecasting/ prediction purpose. Part of the objectives of this research proposal is to extend the research on modeling problem to the situations where we deal with two or more systems of responses which depend on two or more sets of covariates and utilize all the information to provide best fit to responses. This known as seemingly unrelated regressions method is useful in economics, social, biological, epidemiology, engineering and reliability sciences.