Rejoinder on: Minimal penalties and the slope heuristics: a survey
Statistics Theory
2019-10-25 v1 Methodology
Machine Learning
Statistics Theory
Abstract
This text is the rejoinder following the discussion of a survey paper about minimal penalties and the slope heuristics (Arlot, 2019. Minimal penalties and the slope heuristics: a survey. Journal de la SFDS). While commenting on the remarks made by the discussants, it provides two new results about the slope heuristics for model selection among a collection of projection estimators in least-squares fixed-design regression. First, we prove that the slope heuristics works even when all models are significantly biased. Second, when the noise is Gaussian with a general dependence structure, we compute expectations of key quantities, showing that the slope heuristics certainly is valid in this setting also.
Keywords
Cite
@article{arxiv.1909.13499,
title = {Rejoinder on: Minimal penalties and the slope heuristics: a survey},
author = {Sylvain Arlot},
journal= {arXiv preprint arXiv:1909.13499},
year = {2019}
}