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We propose and study a new global test, namely the $F_{\max}$-test, for theone-way ANOVA problem in functional data analysis. The test statistic is takenas the maximum value of the usual pointwise $F$-test statistics over theinterval the functional responses are observed. A nonparametric bootstrapmethod is employed to approximate the null distribution of the test statisticand to obtain an estimated critical value for the test. The asymptotic randomexpression of the test statistic is derived and the asymptotic power isstudied. In particular, under mild conditions, the $F_{\max}$-testasymptotically has the correct level and is root-$n$ consistent in detectinglocal alternatives. Via some simulation studies, it is found that in terms ofboth level accuracy and power, the $F_{\max}$-test outperforms the GlobalizedPointwise F (GPF) test of \cite{Zhang_Liang:2013} when the functional data arehighly or moderately correlated, and its performance is comparable with thelatter otherwise. An application to an ischemic heart real dataset suggeststhat, after proper manipulation, resting electrocardiogram (ECG) signals can beused as an effective tool in clinical ischemic heart screening, without theneed of further stress tests as in the current standard procedure.

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