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

研究者提出了一类具有非凹惩罚似然测量误差的部分线性模型的变量选择方法。所提出的方法可以估计模型中重要变量的系数，同时排除不重要变量。将建立这些估计量的抽样特性。研究者还扩展了惩罚最小二乘方法的思想，以稳健的部分线性模型与测量误差，部分线性模型的纵向数据，部分线性单指数模型。将研究所得到的估计量的收敛速度和所得到的估计量与适当选择的调整参数的预言性质。Monte Carlo模拟是进行有限样本性能的研究所提出的程序。所提出的模型和方法的动机是由调查？研究HIV-1 RNA（病毒载量），CD 4 + 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。该项目的结果将有助于在艾滋病研究中确定重要的标志物和追踪疾病进展。所得结果将有助于统计理论在变量选择和半参数推断方面的发展。

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.