The paper here presented was motivated by a case study involving high-dimensional and high-frequency tidal volume traces measured during induced panic attacks. The focus was to develop a procedure to determine the significance of whether a mean curve dominates another one. The key idea of the suggested method relies on preserving the order in mean while reducing the dimension of the data. The observed data matrix is projected onto a set of lower rank matrices with a positive constraint. A multivariate testing procedure is then applied in the lower dimension. We use simulated data to illustrate the statistical properties of the proposed testing procedure. Results on the case study confirm the preliminary hypothesis of the investigators and provide critical support to their overall goal of creating an experimental model of the clinical panic attack in normal subjects.