The investigator proposes a class of variable selection procedures for partially linear models with measurement errors using non concave penalized likelihood. The proposed procedures can estimate the coefficients of significant variables in the model and simultaneously exclude the insignificant ones. The sampling properties of these estimators will be established. The investigator also extends the ideas of the penalized least squares approaches to robust partially linear models with measurement errors, partially linear models for longitudinal data, and partially linear single index models. The rates of convergence of the resulting estimators and the oracle properties for the resulting estimators with proper choice of the tuning parameters will be investigated. Monte Carlo simulations are to be conducted to examine the finite sample performance of the proposed procedures.
The proposed models and methods are motivated by the investigator?s study of the role of HIV-1 RNA (viral load), CD4+ T cell count, and other potentially useful biomarkers in HIV/AIDS clinical trials. The results of this project will help to identify important markers and trace the disease progressing in AIDS research. The theoretic results will contribute to the advancement of the statistical theory on variable selections and semiparametric inference.
