Grant: Discovery Grants Program - Individual

Currently, the data frequently arise in almost all scientific disciplines such as biology, medical science, biomedical engineering, environmental engineering etc. Moreover, 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 and the resulting approaches will be used in a broad range of applications. The long-term objectives of the present research proposal are to make novel, useful contributions of statistical theory and applications to the broad fields of science and technology. The main purpose of this program is to achieve the advances in the statistical analysis for complex data through the development of an innovative methodology and algorithm in the semi-parametric and nonparametric censored longitudinal quantile regression framework, univariate/multivariate generalized linear models and functional data analysis and to engage highly qualified personnel in these aspects of this research proposal. In the short term, I am proposing to continue my research undertaken during my current NSERC discovery grant with a particular emphasis on achieving the following objectives: (i) developing the estimating method for semiparametric partial linear time-varying-coefficient quantile regression model for longitudinal/survival data and deriving the computational algorithm of estimation and asymptotic properties of estimators for parametric parameters and nonparametric functions; (ii) advancing the innovative adaptive approaches of variable selection for such censored longitudinal quantile regression model and the computational algorithm and asymptotic properties for the proposed estimates; (iii) proposing the novel adaptive weighted aggregation of model screening  and attaining the asymptotical properties for bivariate time-varying-coefficient quantile regression based on longitudinal/survival data; (iv) establishing the univariate/multivariate zero-inflated Lindley binomial mixed model to analyze the longitudinal proportional data and developing the new methodology and computational algorithm for the inference based on such model; (v) exploring the techniques combining the proportional regression and machine learning and the model averaging approach for the zero-inflated over-dispersed proportional data; (vi) investigating the test method for the equivalence of quantile functions and the kernel estimation of quantile functions for gene expression data. In the proposed program, the outcomes include (a) the advancement of knowledge in statistical analysis of complex data that can be applied to many  research fields by other scientists; and (2) the training of HQP equipped with  new ideals and powerful skills for building suitable statistical models to solve real world problems, particularly with  a concentration on developing the statistical talents of diverse peoples under the EDI principle.