A New Test for One-Way ANOVA with Functional Data and Application to Ischemic Heart Screening

TL;DR

This paper introduces the $F_{max}$-test for one-way ANOVA in functional data, demonstrating its superior performance in simulations and real ECG data application for ischemic heart screening.

Contribution

It proposes a novel $F_{max}$-test for functional ANOVA, with theoretical properties and practical advantages over existing methods.

Findings

$F_{max}$-test outperforms GPF test in correlated data scenarios.

The test maintains correct level and is root-$n$ consistent.

Application shows ECG signals can effectively screen for ischemic heart disease.

Abstract

We propose and study a new global test, namely the $F_{\max}$-test, for the one-way ANOVA problem in functional data analysis. The test statistic is taken as the maximum value of the usual pointwise $F$-test statistics over the interval the functional responses are observed. A nonparametric bootstrap method is employed to approximate the null distribution of the test statistic and to obtain an estimated critical value for the test. The asymptotic random expression of the test statistic is derived and the asymptotic power is studied. In particular, under mild conditions, the $F_{\max}$-test asymptotically has the correct level and is root-$n$ consistent in detecting local alternatives. Via some simulation studies, it is found that in terms of both level accuracy and power, the $F_{\max}$-test outperforms the Globalized Pointwise F (GPF) test of \cite{Zhang_Liang:2013} when the functional data are highly or moderately correlated, and its performance is comparable with the latter otherwise. An application to an ischemic heart real dataset suggests that, after proper manipulation, resting electrocardiogram (ECG) signals can be used as an effective tool in clinical ischemic heart screening, without the need of further stress tests as in the current standard procedure.