arXiv subjects

Jeong Min Jeon

Publications and source records attributed to Jeong Min Jeon.

8 recordsLinked to original sources

arXiv2026

A note on a local entropy condition in the Wasserstein space

Entropy conditions are widely used in empirical-process analyses to establish asymptotic properties of M-estimators. In regression problems with responses taking values in a general metric space, a commonly imposed condition requires the entropy integral associated with a shrinking ball centered at the target object to remain uniformly bounded as the ball radius tends to zero. We show that this condition generally fails in the quadratic Wasserstein space of univariate probability distributions supported on a compact interval. Specifically, when the target object is a strictly increasing and absolutely continuous distribution function whose derivative is bounded away from zero and infinity, the corresponding entropy integral diverges as the ball radius tends to zero. The same divergence persists even when the ambient space is restricted to the class of distribution functions satisfying fixed uniform two-sided Lipschitz bounds. These results indicate that different asymptotic analyses are required for the quadratic Wasserstein space.

math.ST↗

arXiv2026

Local Fréchet Regression with Riemannian Predictors

Fréchet regression is well developed for Euclidean predictors, but local linear methods remain limited for general manifold-valued predictors. We propose local constant and local linear estimators for predictors lying on a general Riemannian manifold and responses taking values in a general metric space. The proposed local linear estimator is the first local linear Fréchet regression method in this setting. Our construction uses geodesic neighborhoods, logarithmic-map coordinates, volume-density correction, and frame-invariant scalar equivalent weights. For both estimators, we establish not only pointwise consistency and convergence rates but also uniform consistency and convergence rates. Simulations and real data applications demonstrate the finite-sample performance and practical applicability of the proposed methods across diverse predictor and response geometries.

stat.ME↗

arXiv2026

Functional Principal Component Analysis for Manifold-Indexed Data

Functional principal component analysis (FPCA) is a central tool for dimension reduction and covariance analysis in functional data analysis. We study FPCA for discretely observed scalar-valued functional data indexed by a compact d-dimensional Riemannian manifold M; that is, each subject is modeled as a random function from M to R. This setting is distinct from manifold-valued functional data, where the function values themselves lie on a manifold. We develop intrinsic kernel estimators for the mean and covariance functions using geodesic distances and a Riemannian volume-density correction. The proposed framework accommodates general subject-specific sampling frequencies and includes both equal-weight-per-observation and equal-weight-per-subject schemes. The uniform stochastic analysis uses VC-type empirical-process conditions for intrinsic kernel classes, together with clustered empirical-process compatibility conditions, allowing non-Lipschitz kernels under the stated assumptions. We establish uniform convergence rates for the mean and covariance estimators, Hilbert-Schmidt and operator-norm error bounds for the estimated covariance operator, and convergence rates for eigenvalues and eigenfunctions via spectral perturbation. The rates show that the sparse-to-dense transition is governed by the intrinsic dimension of the indexing manifold, reducing to the classical one-dimensional boundary when d=1. Simulations on S^1 and S^2 and a SONICOM head-related transfer function analysis illustrate the method and show modest but consistent improvements over a coordinate-based baseline when intrinsic geometry is ignored.

stat.ME↗

arXiv2026

Local Fréchet regression with circular predictors

Fréchet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean responses, our work introduces a novel statistical method for handling random objects with circular predictors. We concentrate on local constant and local linear Fréchet regression, providing rigorous proofs for the upper bounds of both bias and stochastic deviation of the estimators under mild conditions. This research lays the groundwork for broadening the application of Fréchet regression to scenarios involving non-Euclidean covariates, thereby expanding its utility in complex data analysis.

math.ST↗

arXiv2026

Local Fréchet regression with toroidal predictors

We provide the first regression framework that simultaneously accommodates responses taking values in a general metric space and predictors lying on a general torus. We propose intrinsic local constant and local linear estimators that respect the underlying geometries of both the response and predictor spaces. Our local linear estimator is novel even in the case of scalar responses. We further establish their asymptotic properties, including consistency and convergence rates. Simulation studies, together with an application to real data, illustrate the superior performance of the proposed methodology.

stat.ME↗

arXiv2024

Hybrid deep additive neural networks

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large number of parameters, primarily due to their reliance on the linear combination structure. Meanwhile, additive regression has been a popular alternative to linear regression in statistics. In this work, we introduce novel deep neural networks that incorporate the idea of additive regression. Our neural networks share architectural similarities with Kolmogorov-Arnold networks but are based on simpler yet flexible activation and basis functions. Additionally, we introduce several hybrid neural networks that combine this architecture with that of traditional neural networks. We derive their universal approximation properties and demonstrate their effectiveness through simulation studies and a real-data application. The numerical results indicate that our neural networks generally achieve better performance than traditional neural networks while using fewer parameters.

stat.ML↗

arXiv2023

Density estimation and regression analysis on S^d in the presence of measurement error

This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density and regression estimators, and study their asymptotic properties including the rates of convergence and asymptotic distributions. We also provide asymptotic confidence intervals based on the asymptotic distributions of the estimators and on the empirical likelihood technique. We present practical details on implementation as well as the results of numerical studies.

math.ST↗

arXiv2022

Additive regression with general imperfect variables

In this paper, we study an additive model where the response variable is Hilbert-space-valued and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows to cover Euclidean, compositional, functional and density-valued variables. By treating imperfect responses, we can cover functional variables taking values in a Riemannian manifold and the case where only a random sample from a density-valued response is available. This treatment can also be applied in semiparametric regression. Dealing with imperfect predictors allows us to cover various principal component and singular component scores obtained from Hilbert-space-valued variables. For the estimation of the additive model having such variables, we use the smooth backfitting method. We provide full non-asymptotic and asymptotic properties of our regression estimator and present its wide applications via several simulation studies and real data applications.

math.ST↗