Distribution-free performance bounds for potential function rules

Author

Devroye, Luc P. ; Wagner, T.J.

Volume

Issue

fYear

1979

fDate

9/1/1979 12:00:00 AM

Firstpage

601

Lastpage

604

Abstract

In the discrimination problem the random variable $\\theta$ , known to take values in ${1, \\cdots ,M}$ , is estimated from the random vector $X$ . All that is known about the joint distribution of $(X, \\theta)$ is that which can be inferred from a sample $(X_{1}, \\theta_{1}), \\cdots ,(X_{n}, \\theta_{n})$ of size $n$ drawn from that distribution. A discrimination nde is any procedure which determines a decision $\\hat{ \\theta}$ for $\\theta$ from $X$ and $(X_{1}, \\theta_{1}) , \\cdots , (X_{n}, \\theta_{n})$ . For rules which are determined by potential functions it is shown that the mean-square difference between the probability of error for the nde and its deleted estimate is bounded by $A/ \\sqrt {n}$ where $A$ is an explicitly given constant depending only on $M$ and the potential function. The $O(n ^{-1/2})$ behavior is shown to be the best possible for one of the most commonly encountered rules of this type.

Keywords

Nonparametric estimation; Pattern classification; Computer errors; Computer science; Histograms; Kernel; Nearest neighbor searches; Random variables; State estimation; US Department of Defense; Upper bound; Voting;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1979.1056087

Filename

1056087

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=930581