Individual Homogeneity Learning in Density Data Response Additive Models

Zixuan Han, Tao Li (), Jinhong You and Narayanaswamy Balakrishnan
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Zixuan Han: Division of Public Health Sciences, Fred Hutchinson Cancer Center, Seattle, WA 98109, USA
Tao Li: School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai 200433, China
Jinhong You: School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai 200433, China
Narayanaswamy Balakrishnan: Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada

Stats, 2025, vol. 8, issue 3, 1-27

Abstract: In many complex applications, both data heterogeneity and homogeneity are present simultaneously. Overlooking either aspect can lead to misleading statistical inferences. Moreover, the increasing prevalence of complex, non-Euclidean data calls for more sophisticated modeling techniques. To address these challenges, we propose a density data response additive model, where the response variable is represented by a distributional density function. In this framework, individual effect curves are assumed to be homogeneous within groups but heterogeneous across groups, while covariates that explain variation share common additive bivariate functions. We begin by applying a transformation to map density functions into a linear space. To estimate the unknown subject-specific functions and the additive bivariate components, we adopt a B-spline series approximation method. Latent group structures are uncovered using a hierarchical agglomerative clustering algorithm, which allows our method to recover the true underlying groupings with high probability. To further improve estimation efficiency, we develop refined spline-backfitted local linear estimators for both the grouped structures and the additive bivariate functions in the post-grouping model. We also establish the asymptotic properties of the proposed estimators, including their convergence rates, asymptotic distributions, and post-grouping oracle efficiency. The effectiveness of our method is demonstrated through extensive simulation studies and real-world data analysis, both of which show promising and robust performance.

Keywords: heterogeneity; latent group structures; hierarchical agglomerative clustering; post-grouping oracle (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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