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

TL;DR

This paper explores the practical computation and application of the regularized projection depth (RPD) for functional data, demonstrating its effectiveness in shape feature detection and outlier identification through theoretical and numerical analyses.

Contribution

It introduces a random projection-based method for efficiently computing RPD and investigates the impact of its tuning parameter, enhancing functional data analysis techniques.

Findings

RPD effectively captures complex shape features in functional data.

The proposed computation method improves efficiency and accuracy.

RPD outperforms existing methods in outlier detection and classification.

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.