Statistical Inference and Modelling for Complex Data

在现代数据技术时代，数据在生物学、医学、生物医学工程、环境工程、生物科学等几乎所有科学学科中都频繁出现。此外，无处不在的数据以各种复杂格式收集。我提出的研究计划将主要集中在开发统计方法和策略来系统地分析这些复杂的数据。在我的研究中取得的方法和结果将在广泛的应用环境中使用。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。我期望开发估算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、右截后生存变量以及许多协变量组成，因此适合采用分位数分析、联合建模和逆概率加权法的联合技术。同时，我将探索联合分位数模型中参数估计的有效算法。我要追求的第二个目标是功能数据的统计推断和建模。我期望推导出分位数函数估计的推理方法，并考虑估计量的渐近性质。随后，根据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，还可以通过比较不同基因表达谱在多种生物学条件下的分位数功能来研究基因的分类。我还打算提出基于希尔伯特空间概率论和常微分方程的独特技术来评估两个基因的关联。另一个研究方向是利用多元零膨胀广义混合线性模型对含有过多零的多元计数/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希尔伯特空间值随机变量的自归一化和的极限定理。本课题的研究成果可以从功能数据分析的角度来检验统计的渐近性质。从纵向生存数据分析的预期方法将被用于发现某些疾病的医疗费用模式。功能数据的方法将适用于分析时间基因表达数据，并改进上游DNA的结果筛选方法，以寻找可能解释基因簇的基序的共同序列。此外，本文还通过理论和实例为应用研究人员提供了多元零膨胀计数/比例数据的处理方法。

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.