Multi-sample comparison using spatial signs for infinite dimensional data

We consider an analysis of variance type problem, where the sample observations are random elements in infinite dimensional space. This scenario covers case, functions. For such a we propose test based on spatial signs. develop asymptotic implementation as well bootstrap and permutation this investigate their size power properties. compare performance our with that several mean tests for functional data studied literature. Interestingly, not only outperforms non-Gaussian models heavy tails or skewed distributions, but some Gaussian also. Further, also involving contaminated probability distributions. Finally, demonstrate these three real datasets: Canadian weather dataset, spectrometric dataset chemical meat samples orthotic measurements volunteers.