Generalized Partially Additive Models For High-Dimensional Data

研究广义加性部分线性模型（GAPLM），旨在开发高效灵活的估计和推理方法、变量选择程序、模型规格检验和模型结构检验，并研究这些方法在生物医学研究中的应用。具体来说，他(a)正在开发一种真正的方法，能够选择数值稳定的重要参数和非参数分量，即使非参数和参数分量的数量分散；(b)正在为GAPLM开发模型规格测试；(c)研究GAPLM模型结构的确定；(d)研究相关数据的边际GAPLM；(e)应用先进的模型和提出的方法来分析基因数据，以研究某些疾病与基因之间的关系，包括识别癌细胞对不同药物治疗的特征基因表达谱，通过整合基因组遗传变异和基因组标记的知识来预测遗传风险，以及通过下一代测序平台收集的数据验证表观遗传密码。提出的模型和方法的动机是研究者对癌症临床试验中基因和其他潜在有用的生物标志物的研究。该项目的结果可以帮助识别重要的基因表达谱和癌细胞，并追踪癌症研究中的疾病进展。这些理论结果对高维协变量的变量选择和半参数推理的统计理论的发展作出了贡献。

The investigator studies generalized additive partially linear models (GAPLM) with the aim of developing efficient and flexible estimation and inference methods, variable selection procedures,model specification tests, and model structure checks, and studies applications of these methods for biomedical research. Specifically speaking, he (a) is developing a genuine method that is able to select important parametric and nonparametric components that are numerically stable , even when the numbers of the nonparametric and parametric components diverge; (b) is developing model specification tests for GAPLM; (c) studies model structure determination for GAPLM; (d) studies marginal GAPLM for correlated data; and (e) applies the advanced models and proposed methods to analyze gene data for study of the relationship between certain diseases and genes, including the identification of signature gene expression profiles of cancer cells in response to different drug treatments, the prediction of genetic risks through integrating knowledge from genetic variations in the genome and genomic markers, and validation of epigenetic codes from data collected through next generation sequencing platforms.The proposed models and methods are motivated by the investigator's study of gene and other potentially useful biomarkers in cancer clinical trials. The results of this project can help identify important gene expression profiles and cancer cells and trace the disease progression in cancer research. The theoretic results contribute to the advancement of the statistical theory on variable selections and semi-parametric inference with high-dimensional covariates.