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Activity Number: 514
Type: Invited
Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
Sponsor: Noether Award Committee
Abstract #321909
Title: Functional Data Analysis and Beyond
Author(s): Jane-Ling Wang*
Companies: University of California at Davis
Keywords:
Abstract:

Functional data are random functions on an interval or set and they have emerged frequently in modern scientific experiments. The analysis of such data is termed "Functional Data Analysis (FDA)". In this talk, we first give a brief overview of the various types of functional data and the approaches to handle them. Then we demonstrate a unified approach and theory that can handle the different sampling plan and weighing schemes. The theory leads to interesting types of asymptotic behavior depending on the sampling plan, which also has an effect on the performance of different weighing schemes. Two commonly adopted weighing schemes will be compared.

Next we show that there is a close connection between high-dimensional and functional data. For instance, densely observed functional data can be viewed as high-dimensional data endowed with a natural ordering. The opposite question is whether one can find a proper ordering of high-dimensional data so they can be reordered and viewed as functional data. To address this question we employ stringing, a method that takes advantage of the high dimensionality by representing such data as discretized and noisy observations that originate from a hidden smooth stochastic process. Stringing thus transforms high-dimensional data to functional data so that established techniques from functional data analysis can be applied for further statistical analysis. We illustrate the advantage of the stringing methodology through several data sets and show how this motivates a functional Cox model that accommodates functional covariates. Theoretical properties of this functional Cox model will be discussed.


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

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