Discussion of 'Beyond mean regression'

摘要

This very enjoyable article by Thomas Kneib looks at (semiparametric) regression from a very wide perspective, allowing us to model a wide range of features in the response distribution. Specifically, the features under study are quantiles and expectiles, which give access to almost any aspect of the response distribution that one may possibly be interested in, and which include mean and median regression as special cases. In the conclusion of his manuscript, the author mentions that modal regression has purposely been left out of this presentation. The main objective of this discussion will be to provide some hopefully useful contribution in this respect. I will begin with discussing (weighted) modal regression in general (and investigate whether it makes sense to define 'modiles'), and proceed with some thoughts on the feasibility of semiparametric modal regression. I will finish this commentary with some general remarks on other aspects of the paper.