Note on distribution-free estimation of maximum linear separation of two multivariate distributions

Albert Vexler; Aiyi Liu; Enrique F. Schisterman; Chengqing Wu

doi:10.1080/10485250600662260

Note on distribution-free estimation of maximum linear separation of two multivariate distributions

Albert Vexler, Aiyi Liu, Enrique F. Schisterman, Chengqing Wu

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the linear separation of two continuous multivariate distributions. Under mild conditions, the optimal linear separation exists uniquely. A kernel-smoothed approach is proposed to estimate the optimal linear combination and the corresponding separation measure. The proposed method yields consistent estimators allowing the construction of confidence intervals.

Original language	English (US)
Pages (from-to)	145-158
Number of pages	14
Journal	Journal of Nonparametric Statistics
Volume	18
Issue number	2
DOIs	https://doi.org/10.1080/10485250600662260
State	Published - Feb 1 2006
Externally published	Yes

Keywords

Kernel estimation
Linear combination
Measure of separation
Non-parametric Behrens-Fisher problem
Receiver operating characteristic curves
Stress-strength problem

ASJC Scopus subject areas

Mathematics(all)
Statistics and Probability

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title = "Note on distribution-free estimation of maximum linear separation of two multivariate distributions",

abstract = "We consider the linear separation of two continuous multivariate distributions. Under mild conditions, the optimal linear separation exists uniquely. A kernel-smoothed approach is proposed to estimate the optimal linear combination and the corresponding separation measure. The proposed method yields consistent estimators allowing the construction of confidence intervals.",

keywords = "Kernel estimation, Linear combination, Measure of separation, Non-parametric Behrens-Fisher problem, Receiver operating characteristic curves, Stress-strength problem",

author = "Albert Vexler and Aiyi Liu and Schisterman, {Enrique F.} and Chengqing Wu",

year = "2006",

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doi = "10.1080/10485250600662260",

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T1 - Note on distribution-free estimation of maximum linear separation of two multivariate distributions

AU - Vexler, Albert

AU - Liu, Aiyi

AU - Schisterman, Enrique F.

AU - Wu, Chengqing

PY - 2006/2/1

Y1 - 2006/2/1

N2 - We consider the linear separation of two continuous multivariate distributions. Under mild conditions, the optimal linear separation exists uniquely. A kernel-smoothed approach is proposed to estimate the optimal linear combination and the corresponding separation measure. The proposed method yields consistent estimators allowing the construction of confidence intervals.

AB - We consider the linear separation of two continuous multivariate distributions. Under mild conditions, the optimal linear separation exists uniquely. A kernel-smoothed approach is proposed to estimate the optimal linear combination and the corresponding separation measure. The proposed method yields consistent estimators allowing the construction of confidence intervals.

KW - Kernel estimation

KW - Linear combination

KW - Measure of separation

KW - Non-parametric Behrens-Fisher problem

KW - Receiver operating characteristic curves

KW - Stress-strength problem

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Note on distribution-free estimation of maximum linear separation of two multivariate distributions

Abstract

Keywords

ASJC Scopus subject areas

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