Testing constancy in monotone response models

A model in which the response is monotonically related to a given exposure or predictor is considered. This is motivated by dose–response analysis, however it also applies to survival distributions depending on a series of ordered multinomial parameters or, in a more general context, to change-point...

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Bibliographic Details
Published in:Computational statistics & data analysis 2014-04, Vol.72, p.45-56
Main Authors: Colubi, Ana, Domínguez-Menchero, J. Santos, González-Rodríguez, Gil
Format: Article
Language:English
Subjects:
Asymptotic properties
Bootstrap test
Chi-bar-squared tests
Independent and dependent data
Isotonic regression
Order restricted statistical inference
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Summary:A model in which the response is monotonically related to a given exposure or predictor is considered. This is motivated by dose–response analysis, however it also applies to survival distributions depending on a series of ordered multinomial parameters or, in a more general context, to change-point problems. In these contexts, although the monotonicity of the response may be a priori known, it is often crucial to determine whether the relationship is effective in a given interval, in the sense of not being constant. An efficient nonparametric test for the constancy of the regression when it is known to be monotone is developed for both independent and dependent data. The asymptotic null distribution of a test statistic based on the integrated regression function is obtained. The power against local alternatives is investigated, and the improvements with respect to the previous studies in the topic are shown. Some bootstrap procedures for the case of independent and dependent data are developed and employed in several applications.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2013.10.029