COMPSTAT 2016: Start Registration
View Submission - CRoNoS FDA 2016
A0205
Title: Functional data Analysis: From basics to current topics of interest Authors:  Hans-Georg Mueller - University of California Davis (United States) [presenting]
Jane-Ling Wang - University of California Davis (United States)
Abstract: An introduction into the most commonly used methods of FDA. These include Functional Principal Component Analysis (FPCA) and the related concept of modes of variation, which is based on simple statistical notions such as mean and covariance function of a random process that can be inferred from the data. FPCA is an important dimension reduction tool and in sparse data situations can be used to impute functional data that are sparsely observed.Another core topic of FDA is functional regression, where one pairs functions or scalars as predictors with responses that are also functions or scalars. For the case where the predictors include functions, a difficult step that requires regularization is the inversion of a covariance operator, which is an ill-posed problem. Such an inverse problem is also related to some forms of functional correlation, which will be another core topic. Nonlinear methods have also found increasing interest. These include polynomial and quadratic regression relations, dimension reduction methods such as additive, continuously additive and index models, and other nonlinear approaches. Further topics of interest that may be covered are warping and manifold learning, the learning of time dynamics from observed realizations of the underlying stochastic process, multivariate and repeatedly observed functional data and stringing of high-dimensional data into functional data.