arXiv subjects

Yuko Araki

Publications and source records attributed to Yuko Araki.

2 recordsLinked to original sources

arXiv2026

Nonlinear Modal Interval Regression for Bivariate Data Analysis

The dispersion of real data is particularly important to understand the variability of a given distribution. In addition to the central tendency, variability is of considerable interest in a wide variety of fields such as life sciences, meteorology, and economics. The modal interval (MI) describes the dispersion or spread of distribution and represents the most concentrated interval of a univariate unimodal distribution. In this study, we propose a nonlinear modal interval regression (MIR) method to smoothly estimate a conditional MI to provide a robust description of how the dispersion of a data distribution varies with the covariate. First, we use kernel density estimation (KDE) to estimate the quantile levels corresponding to the conditional MI bounds, which serve as input to the quantile loss function. Second, we fit upper and lower bound functions using the quantile loss with smoothing splines. The results of numerical experiments demonstrate that the reformulated MIR achieved higher accuracy and stability than both the conventional MIR and the KDE methods. To evaluate the effectiveness of the proposed approach, we applied the method to neonatal hormone data and identified notable rhythms in cortisol and melatonin levels during the first ten days after birth.

stat.ME↗

arXiv2025

Functional Time Series Forecasting of Distributions: A Koopman-Wasserstein Approach

We propose a novel method for forecasting the temporal evolution of probability distributions observed at discrete time points. Extending the Dynamic Probability Density Decomposition (DPDD), we embed distributional dynamics into Wasserstein geometry via a Koopman operator framework. Our approach introduces an importance-weighted variant of Extended Dynamic Mode Decomposition (EDMD), enabling accurate, closed-form forecasts in 2-Wasserstein space. Theoretical guarantees are established: our estimator achieves spectral convergence and optimal finite-sample Wasserstein error. Simulation studies and a real-world application to U.S. housing price distributions show substantial improvements over existing methods such as Wasserstein Autoregression. By integrating optimal transport, functional time series modeling, and spectral operator theory, DPDD offers a scalable and interpretable solution for distributional forecasting. This work has broad implications for behavioral science, public health, finance, and neuroimaging--domains where evolving distributions arise naturally. Our framework contributes to functional data analysis on non-Euclidean spaces and provides a general tool for modeling and forecasting distributional time series.

stat.AP↗