Statistical Inference and Modelling for Complex Data

在现代数据技术时代，数据频繁出现在生物学、医学、生物医学工程、环境工程和生物科学等几乎所有科学学科中，而且无处不在的数据以各种复杂的格式收集。我提出的研究计划将主要集中在开发统计方法和策略，以系统地分析这些复杂的数据。我的研究方法和结果将在广泛的应用背景下得到应用。我的研究兴趣之一将集中在具有时间独立/依赖协变量的纵向生存数据的分位数分析。我期望开发出估计历史过程的分位数函数和累积分位数函数的方法。由于数据可能由纵向变量(S)、右删失生存变量(S)以及多个协变量组成，因此宜采用分位数分析、联合建模和逆概率加权相结合的方法。同时，将探索计算联合分位数模型中参数估计的有效算法。我将追求的第二个目标是对功能数据进行统计推断和建模。我期望得到分位数函数估计的推论方法，并考虑估计量的渐近性质。随后，基于分位数分析得到的估计量，不仅可以研究基因表达谱的行为，而且可以通过比较不同基因表达谱在多种生物条件下的分位数函数来研究基因的分类。我还打算提出基于希尔伯特空间中的概率理论和常微分方程式来评估两个基因的关联的独特技术。另一个研究兴趣是通过多元零膨胀广义混合线性模型对具有过多零点的多变量计数/比例数据进行建模和假设检验。此外，我将继续集中于实值和Hilbert空间值随机变量的自归一化和的极限定理。这方面的研究成果完全可以用来检验函数数据分析中统计量的渐近性质。从纵向生存数据分析中预期的方法将被用来发现某些疾病的医疗费用模式。功能数据的方法论将适合于分析时间基因表达数据，并改进上游DNA结果筛选的方法，以寻找可能解释基因簇的共同基序序列。此外，通过理论和实例，使应用研究人员能够获得多元零膨胀计数/比例数据的程序。

In the modern data technology time, data frequently arise in almost all scientific disciplines such as biology, medical science, biomedical engineering, environmental engineering and bioscience, etc. Moreover, the ubiquitous data are collected in various complex formats. My proposed research program will mainly focus on developing statistical methods and strategies to systematically analyze such complex data. The approaches and results achieved in my research will be used in a broad range of application settings.One of my research interests will focus on the quantile analysis for the longitudinal-survival data with time-independent/dependent covariates. I expect to develop the methods to estimate quantile functions and cumulative quantile functions for history process. Since the data may consist of longitudinal variable(s), right censored survival variable(s) as well as many covariates, it is suitable to use the united technique of quantile analysis, joint modeling and inverse probability weighting method. Meanwhile, I will explore efficient algorithms to compute the estimates of parameters in joint quantile model. The second goal I will pursue is statistical inference and modeling for functional data. I anticipate to derive the inferential methods for estimations of the quantile functions and to consider the asymptotic properties of the estimators. Subsequently, based on the estimators obtained in quantile analysis, not only the behaviors of gene expression profiles can be investigated but also the classification of genes can be studied by comparing the quantile functions for different gene expression profiles under the multiple biological conditions. I also intend to propose unique techniques to assess the association of two genes based on the probability theory in Hilbert space and ordinary differential equation. Another research interest is the modelling and hypotheses testing for multivariate count/proportional data with excessive zeros via multivariate zero-inflated generalized mixed linear model. Furthermore, I will continue concentrating on the limit theorems for self-normalized sums of real valued and Hilbert space valued random variables. The research results on this topic can definitely be exploited to examine the asymptotic properties of statistics from the functional data analysis.The expected approaches from the analysis of longitudinal-survival data will be used to find the patterns of medical cost for some diseases. The methodology for functional data will be appropriate to analyze the temporal gene expression data and to improve the ways to the consequence screening of upstream DNA for the common sequences of motifs that might explain the gene clusters. Moreover, the procedures for the multivariate zero-inflated count/proportional data will be accessible to the applied researchers through the theory and the practical examples.