Testing Constancy for Isotonic Regressions

In this paper, we propose a bootstrap method for testing the constancy of an isotonic regression. The technique we develop is completely non-parametric and enlarges the applicability of the classical chi-bar-squared tests, which require normality assumptions. We prove that our procedure is asymptoti...

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Bibliographic Details
Published in:Scandinavian journal of statistics 2006-09, Vol.33 (3), p.463-475
Main Authors: COLUBI, ANA, SANTOS DOMÍNGUEZ-MENCHERO, J., GONZÁLEZ-RODRÍGUEZ, GIL
Format: Article
Language:English
Subjects:
Bootstrap method
bootstrap test
chi-bar-squared tests
Distribution functions
Exact sciences and technology
isotonic regression
Isotonicity
Linear inference, regression
Linear regression
Mathematical functions
Mathematics
Nonparametric inference
order restricted statistical inference
P values
Perceptron convergence procedure
Probability and statistics
Random variables
Sciences and techniques of general use
Significance level
Statistical methods
Statistical theories
Statistical variance
Statistics
Studies
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Summary:In this paper, we propose a bootstrap method for testing the constancy of an isotonic regression. The technique we develop is completely non-parametric and enlarges the applicability of the classical chi-bar-squared tests, which require normality assumptions. We prove that our procedure is asymptotically correct and consistent. Moreover, by means of simulations we show that it behaves suitably in practice, and similarly to the chi-bar-squared tests under normality. Finally, we illustrate the method with the study of a real case that is well known in the related literature.
ISSN:0303-6898
1467-9469
DOI:10.1111/j.1467-9469.2006.00493.x