Distribution-Free Interval-Wise Inference for Functional-on-Scalar Linear Models
Monday 26th January 2015
Abramowicz, K.; de Luna, S.; Häger, C.; Pini, A.; Schelin, L.; Vantini, S.
We introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed effects. The procedure does not only test the global hypothesis on all the domain, but also selects the intervals where statistically significant effects are detected. We prove that the proposed tests are provided with an asymptotic interval-wise control of the family-wise error rate, i.e., the probability of falsely rejecting any interval of true null hypotheses. The procedure is then applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals, taking individual-specific covariates into account.