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Correlation tests for nonlinear alternatives


Barbour, A D; Costi, M (1993). Correlation tests for nonlinear alternatives. Royal Statistical Society. Journal. Series B: Statistical Methodology, 55(2):541-548.

Abstract

A new class of statistics for detecting association between two variables is proposed. The statistics improve on traditional correlation coefficients by being sensitive to U-shaped and other non-linear relationships between the variables. If both variables are one dimensional, they can be simply defined in terms of ranks, so that their null distributions can in principle be tabulated. Asymptotic discrimination of order n<sup>-1/2</sup> is obtained for any alternative of a continuous functional relationship between the variables. Power against trend alternatives is investigated by simulation.

A new class of statistics for detecting association between two variables is proposed. The statistics improve on traditional correlation coefficients by being sensitive to U-shaped and other non-linear relationships between the variables. If both variables are one dimensional, they can be simply defined in terms of ranks, so that their null distributions can in principle be tabulated. Asymptotic discrimination of order n<sup>-1/2</sup> is obtained for any alternative of a continuous functional relationship between the variables. Power against trend alternatives is investigated by simulation.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1993
Deposited On:12 Apr 2010 12:10
Last Modified:05 Apr 2016 13:28
Publisher:Wiley-Blackwell
ISSN:0035-9246
Free access at:Related URL. An embargo period may apply.
Related URLs:http://www.jstor.org/stable/2346213
http://user.math.uzh.ch/barbour/pub/Barbour/BCosti.pdf (Author)

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