Statistical Inference and Modelling for Complex Data

在现代数据技术时代，数据频繁地出现在几乎所有的科学学科中，如生物学、医学、生物医学工程、环境工程和生物科学等，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，系统地分析这些复杂的数据。我的研究方法和结果将被广泛应用于各种应用环境中，我的研究兴趣之一将集中在具有时间独立/依赖协变量的患者生存数据的分位数分析。 我希望能开发出一种方法来估算 分位数函数和累积分位数函数。由于数据可能包含纵向变量、右删失生存变量以及多个协变量，因此适合使用分位数分析、联合建模和逆概率加权法的联合技术。同时，我将探索计算联合分位数模型参数估计的有效算法。我将追求的第二个目标是函数数据的统计推断和建模。我期望得到估计的分位数函数的推断方法，并考虑估计量的渐近性质。随后，基于分位数分析中获得的估计，不仅可以研究基因表达谱的行为，而且可以通过比较在多种生物条件下不同基因表达谱的分位数函数来研究基因的分类。我还打算提出独特的技术来评估两个基因的关联的基础上的概率理论在希尔伯特空间和常微分方程。另一个研究兴趣是通过多元零膨胀广义混合线性模型对多变量计数/比例数据进行建模和假设检验。此外，我将继续集中在真实的值和Hilbert空间值随机变量的自正规和的极限定理。这一课题的研究成果可以用于检验统计量的渐近性质，从函数数据分析中得到预期的方法，从患者生存数据分析中得到预期的方法，以发现某些疾病的医疗费用模式。功能数据的方法将是适当的，以分析时间的基因表达数据，并改善的方式，结果筛选的上游DNA的共同序列的基序，可能解释基因簇。此外，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.