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Robust comparison of regression curves

Author

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  • Long Feng
  • Changliang Zou
  • Zhaojun Wang
  • Lixing Zhu

Abstract

This paper is concerned about robust comparison of two regression curves. Most of the procedures in the literature are least-squares-based methods with local polynomial approximation to nonparametric regression. However, the efficiency of these methods is adversely affected by outlying observations and heavy-tailed distributions. To attack this challenge, a robust testing procedure is recommended under the framework of the generalized likelihood ratio test (GLR) by incorporating with a Wilcoxon-type artificial likelihood function. Under the null hypothesis, the proposed test statistic is proved to be asymptotically normal and free of nuisance parameters and covariate designs. Its asymptotic relative efficiency with respect to the least-squares-based GLR method is closely related to that of the signed-rank Wilcoxon test in comparison with the $$t$$ t test. We then consider a bootstrap approximation to determine $$p$$ p values of the test in finite sample situation. Its asymptotic validity is also presented. A simulation study is conducted to examine the performance of the proposed test and to compare it with its competitors in the literature. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Long Feng & Changliang Zou & Zhaojun Wang & Lixing Zhu, 2015. "Robust comparison of regression curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 185-204, March.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:1:p:185-204
    DOI: 10.1007/s11749-014-0394-2
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    References listed on IDEAS

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    1. H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    2. Shang, Suoping & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression for semiparametric varying-coefficient models," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1815-1822.
    3. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    4. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 36-48.
    5. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    6. Terpstra, Jeff T. & McKean, Joseph W., 2005. "Rank-Based Analysis of Linear Models Using R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i07).
    7. Delgado, Miguel A., 1992. "Testing the equality of nonparametric regression curves," UC3M Working papers. Economics 2826, Universidad Carlos III de Madrid. Departamento de Economía.
    8. Holger Dette & Jens Wagener & Stanislav Volgushev, 2011. "Comparing Conditional Quantile Curves," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 63-88, March.
    9. Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, University Library of Munich, Germany.
    10. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    11. Robbins, Michael W. & Lund, Robert B. & Gallagher, Colin M. & Lu, QiQi, 2011. "Changepoints in the North Atlantic Tropical Cyclone Record," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 89-99.
    12. Holger Dette & Jens Wagener & Stanislav Volgushev, 2013. "Nonparametric comparison of quantile curves: a stochastic process approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 243-260, March.
    13. Zhang, Chunming, 2003. "Calibrating the Degrees of Freedom for Automatic Data Smoothing and Effective Curve Checking," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 609-628, January.
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    Cited by:

    1. Jun Zhang & Zhenghui Feng & Xiaoguang Wang, 2018. "A constructive hypothesis test for the single-index models with two groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1077-1114, October.
    2. Kathrin Möllenhoff & Frank Bretz & Holger Dette, 2020. "Equivalence of regression curves sharing common parameters," Biometrics, The International Biometric Society, vol. 76(2), pages 518-529, June.
    3. Boente, Graciela & Pardo-Fernández, Juan Carlos, 2016. "Robust testing for superiority between two regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 151-168.
    4. Cuizhen Niu & Lixing Zhu, 2018. "A robust adaptive-to-model enhancement test for parametric single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1013-1045, October.

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