Robust Functional ANOVA with Application to Additive Manufacturing

TL;DR

This paper introduces RoFANOVA, a robust nonparametric functional ANOVA method designed to handle outliers in functional data, demonstrated through simulations and a real additive manufacturing case study.

Contribution

The paper presents a novel robust functional ANOVA approach using a permutation test and M-estimator extension, improving outlier resistance in functional data analysis.

Findings

RoFANOVA outperforms existing methods in simulations.

Effective in detecting differences in group functional means.

Successfully applied to additive manufacturing data.

Abstract

The development of data acquisition systems is facilitating the collection of data that are apt to be modelled as functional data. In some applications, the interest lies in the identification of significant differences in group functional means defined by varying experimental conditions, which is known as functional analysis of variance (FANOVA). With real data, it is common that the sample under study is contaminated by some outliers, which can strongly bias the analysis. In this paper, we propose a new robust nonparametric functional ANOVA method (RoFANOVA) that reduces the weights of outlying functional data on the results of the analysis. It is implemented through a permutation test based on a test statistic obtained via a functional extension of the classical robust $ M $-estimator. By means of an extensive Monte Carlo simulation study, the proposed test is compared with some alternatives already presented in the literature, in both one-way and two-way designs. The performance of the RoFANOVA is demonstrated in the framework of a motivating real-case study in the field of additive manufacturing that deals with the analysis of spatter ejections. The RoFANOVA method is implemented in the R package rofanova, available online at https://github.com/unina-sfere/rofanova.