Research

Paper

TESTING February 26, 2026

Projection depth for functional data: Practical issues, computation and applications

Authors

Filip Bočinec, Stanislav Nagy, Hyemin Yeon

Abstract

Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the recently proposed regularized projection depth (RPD), which induces a meaningful ordering of functional data while appropriately accommodating their complex shape features. Specifically, we examine the impact and choice of its tuning parameter, which regulates the degree of effective dimension reduction applied to the data, and propose a random projection-based approach for its efficient computation, supported by theoretical justification. Through comprehensive numerical studies, we explore a wide range of statistical applications of the RPD and demonstrate its particular usefulness in uncovering shape features in functional data analysis. This ability allows the RPD to outperform competing depth-based methods, especially in tasks such as functional outlier detection, classification, and two-sample hypothesis testing.

Metadata

arXiv ID: 2602.22877
Provider: ARXIV
Primary Category: stat.ME
Published: 2026-02-26
Fetched: 2026-02-27 04:35

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