An L2 point of view in testing monotone regression

In this paper, we propose a new approach to test isotonic regression based on the L2-distance from a regression estimator to the set of all nondecreasing functions. This distance represents a natural measure of nondecrease and it provides a completely nonparametric test. The procedure is analyzed in...

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Bibliographic Details
Published in:Journal of nonparametric statistics 2005-03, Vol.17 (2), p.135-153
Main Authors: Dominguez-Menchero, J Santos, Gonzalez-Rodriguez, Gil, Lopez-Palomo, Maria Jesus
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper, we propose a new approach to test isotonic regression based on the L2-distance from a regression estimator to the set of all nondecreasing functions. This distance represents a natural measure of nondecrease and it provides a completely nonparametric test. The procedure is analyzed in fixed design models allowing more than one observation per design point. Up to now, only x-2-tests could be applied in this context, and these classical tests require normality of conditional distributions, as well as important restrictions on the variances and complex calculations when being carried out. In contrast, the nonparametric technique that we present does not require any restriction on the conditional variances and it is very simple to implement. In addition, its power under normality assumptions is similar to that of the classical X-2-tests.
ISSN:1048-5252
DOI:10.1080/10485250410001722288