@inproceedings{a5665e44dacc4827bf4e7bef6c8d33b8,
title = "Competing against the best nearest neighbor filter in regression",
abstract = "Designing statistical procedures that are provably almost as accurate as the best one in a given family is one of central topics in statistics and learning theory. Oracle inequalities offer then a convenient theoretical framework for evaluating different strategies, which can be roughly classified into two classes: selection and aggregation strategies. The ultimate goal is to design strategies satisfying oracle inequalities with leading constant one and rate-optimal residual term. In many recent papers, this problem is addressed in the case where the aim is to beat the best procedure from a given family of linear smoothers. However, the theory developed so far either does not cover the important case of nearest-neighbor smoothers or provides a suboptimal oracle inequality with a leading constant considerably larger than one. In this paper, we prove a new oracle inequality with leading constant one that is valid under a general assumption on linear smoothers allowing, for instance, to compete against the best nearest-neighbor filters.",
keywords = "adaptive smoothing, nonparametric regression, supervised learning",
author = "Dalalyan, \{Arnak S.\} and Joseph Salmon",
year = "2011",
month = oct,
day = "20",
doi = "10.1007/978-3-642-24412-4\_13",
language = "English",
isbn = "9783642244117",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "129--143",
booktitle = "Algorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings",
note = "22nd International Conference on Algorithmic Learning Theory, ALT 2011 ; Conference date: 05-10-2011 Through 07-10-2011",
}