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Testing strict monotonicity in nonparametric regression

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  • Birke, Melanie
  • Dette, Holger

Abstract

A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the ?true? regression function is strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis of strict monotonicity.

Suggested Citation

  • Birke, Melanie & Dette, Holger, 2006. "Testing strict monotonicity in nonparametric regression," Technical Reports 2006,49, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200649
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    References listed on IDEAS

    as
    1. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    2. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
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    Cited by:

    1. Pramita Bagchi & Subhra Sankar Dhar, 2020. "A study on the least squares estimator of multivariate isotonic regression function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1192-1221, December.
    2. Birke, Melanie, 2006. "Central limit theorems for the integrated squared error of derivative estimators," Technical Reports 2006,53, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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