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Jiaming Qiu, 'Nonparametric estimates for repeated densities with heterogeneous sample sizes', TADS Lunch-n-Learn
Presenter: Jiaming Qiu
Title: Nonparametric estimates for repeated densities with heterogeneous sample sizes
Abstract: We consider the estimation of densities in multiple subpopulations, where the available sample size in each subpopulation varies greatly. For example, in the context of epidemiology, different diseases could share similar generating mechanisms but contrast in their prevalence. A fully data-driven approach is proposed to estimate the density of a quantity of interest in each subpopulation without the need of specifying the parametric form of the density families. The idea is to map the density functions into a Hilbert space and then apply functional data analytic methods so as to derive low-dimensional approximates. Subpopulation densities could then be fitted within the low-dimensional families using likelihood-based methods, where information borrowing is enforced through shrinkage. The proposed methods are illustrated through simulations and applications to electronic medical records, showcasing interpretable estimates and favorable performance.
Bio: Jiaming Qiu is a Ph.D. student in the Department of Statistics at Iowa State University, working under Dr. Xiongtao Dai and Dr. Zhengyuan Zhu. His current research interests include functional data analysis and manifold data analysis. He obtained B.S. in mathematics from Tsinghua University and M.S. in statistics from University of Michigan Ann Arbor.
After the presentation, there will be a short time for discussion and questions afterwards.