Nonlinear Modal Interval Regression for Bivariate Data Analysis

TL;DR

This paper introduces a nonlinear modal interval regression method that uses kernel density estimation and smoothing splines to robustly estimate the dispersion of data conditioned on covariates, improving accuracy over existing methods.

Contribution

The study proposes a novel nonlinear modal interval regression approach that combines KDE and smoothing splines for better dispersion estimation in data analysis.

Findings

Higher accuracy and stability compared to conventional methods

Effective in analyzing neonatal hormone data

Identified significant hormonal rhythms in newborns

Abstract

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.