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Activity Number: 56 - Novel Statistical Methods for Variable Selection with Applications
Type: Topic Contributed
Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #328563 Presentation
Title: Nonlinear Multivariate Functional PCA
Author(s): Jun Song* and Bing Li
Companies: UNC Charlotte and The Pennsylvania State University
Keywords: functional data analysis; nonlinear dimension reduction; RKHS; PCA; multivariate functional data

In this talk, I will discuss nonlinear dimension reduction for functional data in a supervised way. In particular, the functional data can be a form of multivariate functional data in which multiple functions defined on different time domains are considered to be one observation. First, I will introduce nested reproducing kernel Hilbert (RKHS) space which provides a general mechanism for nonlinear functional data analysis. Two layers of function spaces are constructed in a nested fashion so that the first space represents the observed functional data, and the second space characterizes nonlinearity of the random functions. Then I will introduce a method of nonlinear functional additive PCA, the detailed procedure for estimation, and its consistency and convergence rate. The simulation studies and applications to real data will be introduced at the end.

Authors who are presenting talks have a * after their name.

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