Kernel based method for the k-sample problem with functional data

Abstract

In this paper, we deal with the problem of testing for the equality of k probability distributions defined on $(\mathcal{X},\mathcal{B}),$ where $\mathcal{X}$ is a metric space and $\mathcal{B}$ is the corresponding Borel σ-field. We introduce a test statistic based on reproducing kernel Hilbert space embeddings and derive its asymptotic distribution under the null hypothesis. Simulations show that the introduced procedure outperforms a known method.

Keywords:

• Hypothesis testing
• k-sample problem
• reproducing kernel Hilbert space
• functional data
• asymptotic distribution