CAREER: New Topics in Functional Data Analysis

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Functional data are random vectors in a functional space, which are usually observed on discrete points and measured with error. Functional data are also deeply connected to other types of correlated data, such as spatial data, since they can both be modeled as stochastic processes. In the proposed research, the investigator will broaden the applications of functional data analysis by proposing a new functional data approach to model spatio-temporal point pattern data from disease surveillance applications, where the spatio-temporal random effects are modeled as latent functional processes. Motivated by scientific problems in colon carcinogenesis experiments and hypertension studies, the investigator proposes new dimension reduction methods, which are widely applicable to semiparametric regression problems with functional predictors. The investigator proposes new estimation procedures based on spline approximation and roughness penalties, and will also investigate the model selection and inference problems related to these methods. The investigator also proposes to model longitudinal clinical trial data by the functional analysis of covariance models, where different treatment effects are represented by nonparametric functions in time. The proposed nonparametric hypothesis test can be used to detect the treatment effects. Specifically, the investigator will study the effect of the within-subject correlation on the power of the test.The proposed functional data approach to disease surveillance data will help to model the relationship between disease occurrence and some environmental variables (such as pollution level), estimate the time trend in the disease rate, and predict the unknown risk factors represented by latent random effects. The results will help disease control agencies and local officials to gain better understanding of the disease risk and develop better public health policies, such as emission or water quality control policies. The proposed dimension reduction methods provide the much needed statistical tools in the semiparametric regression problems in colon carcinogenesis and hypertension studies. The proposed nonparametric hypothesis testing procedure for functional analysis of covariance models answers a fundamental question in clinical trials, which is to compare the effectiveness of different treatments. The investigator will provide free and user-friendly software to scientific researchers and incorporate his research activity with graduate education. To further disseminate the research results and motivate new ideas, the investigator will develop a new course on functional data analysis and organize a research workshop.