Comments on: Model-free model-fitting and predictive distributions

I first of all wish to congratulate the author for this inspiring and interesting article. It offers a new, fresh view on how to construct prediction intervals in regression, and it also allows for many extensions beyond the framework of regression. Apart from proposing a novel and promising idea, the article is also a very rich source of references, not only on the topic of prediction intervals, but also on related topics like transformation models, bootstrap, and nonparametric regression. The paper also contains interesting side-comments and links with other areas in the literature, giving hence a very complete picture of the problem considered in the paper. In this comment I would like to discuss briefly an outlook on two possible further topics of research. The first one is on the construction of prediction intervals when endogeneity is present, and the second one is on the theoretical investigation of the proposed intervals.