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Testing for one-sided alternatives in nonparametric censored regression

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  • Cédric Heuchenne
  • Juan Pardo-Fernández

Abstract

Assume that we have two populations (X 1 ,Y 1 ) and (X 2 ,Y 2 ) satisfying two general nonparametric regression models Y j =m j (X j )+ε j , j=1,2, where m(⋅) is a smooth location function, ε j has zero location and the response Y j is possibly right-censored. In this paper, we propose to test the null hypothesis H 0 :m 1 =m 2 versus the one-sided alternative H 1 :m 1 >m 2 . We introduce two test statistics for which we obtain the asymptotic normality under the null and the alternative hypotheses. Although the tests are based on nonparametric techniques, they can detect any local alternative converging to the null hypothesis at the parametric rate n −1/2 . The practical performance of a bootstrap version of the tests is investigated in a simulation study. An application to a data set about unemployment duration times is also included. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Cédric Heuchenne & Juan Pardo-Fernández, 2012. "Testing for one-sided alternatives in nonparametric censored regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 498-518, September.
    • Handle: RePEc:spr:testjl:v:21:y:2012:i:3:p:498-518
    DOI: 10.1007/s11749-011-0260-4
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    References listed on IDEAS

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    1. Srihera, Ramidha & Stute, Winfried, 2010. "Nonparametric comparison of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2039-2059, October.
    2. Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2006. "Comparison of Regression Curves with Censored Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 409-434, September.
    3. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
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