Flexible modelling of functional data

点击翻译按钮获取中文摘要

The proposed research focuses on the development of methodologies and theory on two important aspects of functional data analysis: 1) functional regression analysis; 2) joint modelling of generalized longitudinal data and survival time. The first project is to develop methodologies for a new class of models, Functional Additive Models, which in certain sense unify and generalize functional regression analysis. In this new framework, the regression of the scalar or functional response on functional predictor is not restricted to linear operator, which allows the data "speak" for themselves. Comprehensive investigation will be carried out, including model estimation and selection, theory, inference, applications and potential extensions. The second emphasis of this proposal is to jointly model the generalized type of longitudinal data and survival time. This is motivated by the fact that in many clinical trials longitudinal observations are not necessarily continuous, but may be categorical, such as binomial or Poisson outcomes, while most existing approaches deal with continuous longitudinal data. I will present a new perspective from functional data viewpoint, where functional principal component techniques will be exploited to achieve dimension reduction. Automatic algorithms and inference procedures will be developed, which take Monte Carlo error and optimal stopping rules into account. This proposal is motivated by my ongoing and future research collaborations with biologists and physicians. The new approaches will be applied to the datasets generated from these collaborations and will provide useful guidance for future experiments. The procedures developed will be applicable for general functional data from various disciplines, which in turn facilitate the advancement of many scientific fields.