🤖 AI Summary
This paper addresses binary classification for continuous-time functional data. We propose a probabilistic binary classification (PBC) criterion grounded in inter-functional distances, along with a fully nonparametric estimation procedure. Unlike conventional paradigms relying on ordered scalar labels, PBC directly quantifies similarity between an individual’s trajectory and the functional mean of the positive group—bypassing structural assumptions or dimensionality reduction on functional biomarkers. The method integrates functional data analysis, nonparametric kernel estimation, and Monte Carlo simulation, implemented in R. Simulation studies and real-data analyses demonstrate that PBC exhibits strong robustness under moderate sample sizes and achieves significantly higher classification accuracy than state-of-the-art competitors—particularly in challenging settings involving high-dimensional, nonstationary, and small-sample functional biomarkers.
📝 Abstract
The adequate use of information measured in a continuous manner along a period of time represents a methodological challenge. In the last decades, most of traditional statistical procedures have been extended for accommodating these functional data. The binary classification problem, which aims to correctly identify units as positive or negative based on marker values, is not aside of this scenario. The crucial point for making binary classifications based on a marker is to establish an order in the marker values, which is not immediate when these values are presented as functions. Here, we argue that if the marker is related to the characteristic under study, a trajectory from a positive participant should be more similar to trajectories from the positive population than to those drawn from the negative. With this criterion, a classification procedure based on the distance between the involved functions is proposed. Besides, we propose a fully non-parametric estimator for this so-called probability-based criterion, PBC. We explore its asymptotic properties, and its finite-sample behavior from an extensive Monte Carlo study. The observed results suggest that the proposed methodology works adequately, and frequently better than its competitors, for a wide variety of situations when the sample size in both the training and the testing cohorts is adequate. The practical use of the proposal is illustrated from real-world dataset. As online supplementary material, the manuscript includes a document with further simulations and additional comments. An R function which wraps up the implemented routines is also provided.