Two-sample tests for multivariate functional data with applications

Investigating spatial scan statistics for multivariate functional data

“…Very recently, Qiu et al (2021) proposed a version of this pointwise test for p-dimensional functional data (p ≥ 2) to compare the mean functions of X in two groups.…”

“…Thus, as previously, in the context of cluster detection, the null hypothesis H 0 can be defined as follows: H 0 : ∀w ∈ W, µ w = µ w c = µ S , where µ w , µ w c and µ S stand for the mean functions in w, outside w and over S, respectively. And the alternative hypothesis H (w) 1 associated with a potential cluster w can be defined as follows: Qiu et al (2021) proposed to compare the mean function µ w in w with the mean function µ w c in w c by using the following statistic:…”

“…The X i were simulated according to the following model with p = 2 (see Qiu et al, 2021;Martino et al, 2019, for more details):…”

“…Thus we will define new spatial scan statistics for multivariate functional data based on statistical tests for comparing multivariate functional samples. Recently Górecki & Smaga (2017) and Qiu et al (2021) developed respectively a MANOVA test statistic and a functional Hotelling T 2 -test statistic for multivariate functional data. We also propose to consider the multivariate extension of the Wilcoxon rank-sum test developed by Oja & Randles (2004) as a pointwise test statistic.…”

A review of goodness-of-fit tests for models involving functional data

“…Finally, it is worth it to mention the two-sample problem, a common offspring of the simplehypothesis one-sample GoF problem. Two-sample tests have also received a significant deal of attention in the last decades; see, e.g., the recent contributions by Jiang et al (2019) and Qiu et al (2021), and references therein.…”