Statistics and Data Science Seminar: Nonparametric Estimation of Repeated Densities with Heterogeneous Sample Sizes, by Xiongtao Dai
September 29, 2021
4:00 PM - 4:50 PM
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Xiongtao Dai (Iowa State University): Nonparametric Estimation of Repeated Densities with Heterogeneous Sample Sizes
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 the 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.
Sep 28, 2021
Sep 28, 2021