Speaker: Professor Zhenhua Lin
Institute: National University of Singapore
Time/Date: 11-12AM, Thursday, 11 November 2021
Title: Nonparametric Estimation of Repeated Densities with Heterogeneous Sample Sizes
Abstract: Functional data analysis concerns a sample of random functions, such as a collection of body growth trajectories. Dimension reduction tools, such as functional principal component analysis, are available to reduce and represent the infinite-dimensional functions. In this work, we are interested in estimating densities as functions, where each density comes from a subpopulation. For example, in the context of epidemiology, the age distributions of patients with different diseases is of central interest, where each disease defines a subpopulation. A key challenge comes from the highly variable sample sizes for different conditions, making the estimation of age profiles difficult for rare conditions. We propose a fully data-driven approach to estimate the densities without the need of specifying the parametric form of the density families. The idea is to map the density functions to a Hilbert space and then apply functional data analytic methods so as to derive low-dimensional approximates. I will show that the proposed methods yield interpretable results and are efficient for modeling electronic medical records and extreme rainfall.
[Joint work with Jiaming Qiu and Zhengyuan Zhu]
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