Homogeneity test for functional data based on depth measures

In the context of functional data analysis, we propose a new method to test the homogeneity of families of functions. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two families. A simulation study is performed to check the efficiency of the testswhen confronted with shape and magnitude perturbation. Finally, we apply these tools to measure the homogeneity in some families of real data, obtaining good results for these new methods.