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Testing constancy in monotone response models

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  • Colubi, Ana
  • Domínguez-Menchero, J. Santos
  • González-Rodríguez, Gil

Abstract

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.

Suggested Citation

  • Colubi, Ana & Domínguez-Menchero, J. Santos & González-Rodríguez, Gil, 2014. "Testing constancy in monotone response models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 45-56.
    • Handle: RePEc:eee:csdana:v:72:y:2014:i:c:p:45-56
    DOI: 10.1016/j.csda.2013.10.029
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    References listed on IDEAS

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    1. Björn Bornkamp & Katja Ickstadt, 2009. "Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose–Response Analysis," Biometrics, The International Biometric Society, vol. 65(1), pages 198-205, March.
    2. Cécile Durot & Laurence Reboul, 2010. "Goodness‐of‐Fit Test for Monotone Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 422-441, September.
    3. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    4. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    5. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    6. Marschner, Ian C. & Gillett, Alexandra C. & O’Connell, Rachel L., 2012. "Stratified additive Poisson models: Computational methods and applications in clinical epidemiology," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1115-1130.
    7. Ana Colubi & J. Santos Domínguez‐Menchero & Gil González‐Rodríguez, 2006. "Testing Constancy for Isotonic Regressions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 463-475, September.
    8. Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    9. Bhattacharya, Rabi & Lin, Lizhen, 2013. "Recent progress in the nonparametric estimation of monotone curves—With applications to bioassay and environmental risk assessment," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 63-80.
    10. J. Vilar-Fernández & J. Vilar-Fernández & W. González-Manteiga, 2007. "Bootstrap tests for nonparametric comparison of regression curves with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 123-144, May.
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