Distribution free MMD tests for model selection with estimated parameters

Understand

There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification.

• However, they ignore the presence of estimated parameters in the case of composite null hypotheses.
• In this paper, we first illustrate the effect of parameter estimation in model specification tests based on the MMD.
• Second, we propose simple model specification and model selection tests in the case of models with estimated parameters.