Statistical Inference and Modelling for Complex Data

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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.**