Distribution regression model with a Reproducing Kernel Hilbert Space approach

In this paper, we introduce a new distribution regression model for probability distributions. This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework, where universal kernels are built using Wasserstein distances for distributions belonging to and omega is a compact subspace of . We prove the universal kernel property of such kernels and use this setting to perform regressions on functions. Different regression models are first compared with the proposed one on simulated functional data for both one-dimensional and two-dimensional distributions. We then apply our regression model to transient evoked otoascoutic emission (TEOAE) distribution responses and real predictors of the age.