The investigator proposes extensions of existing asymptotic distributional theories for M- and Z-estimations in the semiparametric models with separated parameters to accommodate situations where the estimation criteria for the semiparametric models are parameterized with bundled parameters, i.e. the infinite dimensional parameter is an unknown function of the parameter of interest. The proposal is motivated by several statistical problems including the efficient estimation in the linear regression model with censored data under several different censoring mechanisms, the efficient estimation in the single index model, the partial likelihood estimation in the Cox regression model with an unknown link function, and the weighted estimation for missing data problems in survival analysis. The investigator also proposes to apply the general theory for bundled parameters to all these problems, particularly for the case that the infinite dimensional nuisance parameter is approximated by regression splines.
The proposed research is primarily motivated by PI's collaboration in biomedical studies, where more robust statistical modeling techniques are desirable to reduce the uncertainty of model misspecification, particularly when data are incomplete due to limited study follow-up. The proposed research will also allow the investigator to add more thorough statistical results to the course of advanced survival analysis and be helpful in developing the special topic course on semiparametric models into a regular Ph.D. level course. The proposed research activities will motivate graduate students to become independent researchers who are able to engage in fundamental statistical research.
Normal 0 false false false EN-US ZH-CN X-NONE Statistical inference for semiparametric models with bundled parameters is a challenging problem with very limited literature, whereas the applications of such models are broad. This project has laid the theoretical foundation for such statistical inference. Particularly, we have extended existing asymptotic distributional theories for M- and Z-estimations in the semiparametric models with separated parameters to accommodate situations where the estimation criteria for the semiparametric models are parameterized with bundled parameters. We have also successfully applied the fundamental M- and Z-estimation theories to the efficient estimation in the linear regression model with censored data, i.e. the accelerated failure time model, and to the case-cohort studies with parameters estimated by weighted approach using unpredictable weights, which has been a longstanding technical issue for the development of asymptotic distributions for such estimates. The obtained results will have broad impact on study designs and data analysis in a wide range of health and biomedical research, particularly in large epidemiological cohort studies on chronic diseases. The awarded project has provided research opportunities to graduate students in biomedical and other health research fields. The research is helpful in developing new teaching material for graduate courses at the University Michigan and is disseminated through journal articles and presentations.
