@inbook {IOPORT.05960463,
    author       = {Dalalyan, Arnak S. and Salmon, Joseph},
    title        = {Competing against the best nearest neighbor filter in regression.},
    year         = {2011},
    booktitle    = {Algorithmic learning theory. 22nd international conference, ALT 2011, Espoo, Finland, October 5--7, 2011. Proceedings},
    isbn         = {978-3-642-24411-7},
    pages        = {129-143},
    publisher    = {Berlin: Springer},
    doi          = {10.1007/978-3-642-24412-4_13},
    abstract     = {Summary: 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.},
    identifier   = {05960463},
}