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Activity Number: 5 - New Developments in Functional Data
Type: Invited
Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #322323
Title: Mixture Inner Product Spaces and Their Application to Functional Data Analysis
Author(s): Hans-Georg G Müller* and Fang Yao and Zhenhua Lin
Companies: University of California, Davis and University of Toronto and University of Toronto
Keywords: Functional Data Analysis ; Mixture Model ; Hilbert Space ; Density in Function Space ; Mixture FPCA

We introduce the concept of mixture inner product spaces associated with a given Hilbert space, which feature an infinite-dimensional mixture of finite-dimensional vector spaces and are dense in the underlying Hilbert space. While this concept can be applied to data in any infinite-dimensional Hilbert space, the case of functional data that are random elements in the $L^2$ space of square integrable functions is of special interest. In this mixture space representation, each realization of the underlying stochastic process falls into one of the component spaces and is represented by a finite number of basis functions. This mixture representation provides a new perspective on the construction of a probability density in function space under mild regularity conditions and leads to a mixture functional principal component analysis, where individual trajectories possess a trajectory-specific dimension. We establish estimation consistency of the functional mixture density and introduce an algorithm for fitting the functional mixture model based on a modified expectation-maximization algorithm.

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

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