Development of Model Selection for Semiparametric Models in Analysis of High-Dimensional Data

研究者提出了一类变量选择程序的部分线性模型与测量误差使用非凹惩罚似然。所提出的方法可以估计模型中显著变量的系数，同时排除不显著变量。这些估计器的抽样性质将被建立。研究者还将惩罚最小二乘方法的思想扩展到具有测量误差的鲁棒部分线性模型，纵向数据的部分线性模型和部分线性单指标模型。在适当选择调优参数的情况下，研究了所得估计器的收敛速度以及所得估计器的oracle性质。将进行蒙特卡罗模拟以检验所提出程序的有限样本性能。提出的模型和方法是由研究者的动机？HIV-1 RNA（病毒载量）、CD4+ T细胞计数和其他潜在有用的生物标志物在HIV/AIDS临床试验中的作用的研究。该项目的结果将有助于确定重要的标记物并追踪艾滋病研究中的疾病进展。这些理论结果将有助于统计理论在变量选择和半参数推理方面的发展。

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.