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Nonparametric comparison of regression functions

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  • Srihera, Ramidha
  • Stute, Winfried

Abstract

In this work, we provide a new methodology for comparing regression functions m1 and m2 from two samples. Since apart from smoothness no other (parametric) assumptions are required, our approach is based on a comparison of nonparametric estimators and of m1 and m2, respectively. The test statistics incorporate weighted differences of and computed at selected points. Since the design variables may come from different distributions, a crucial question is where to compare the two estimators. As our main results we obtain the limit distribution of (properly standardized) under the null hypothesis H0:m1=m2 and under local and global alternatives. We are also able to choose the weight function so as to maximize the power. Furthermore, the tests are asymptotically distribution free under H0 and both shift and scale invariant. Several such 's may then be combined to get Maximin tests when the dimension of the local alternative is finite. In a simulation study we found out that our tests achieve the nominal level and already have excellent power for small to moderate sample sizes.

Suggested Citation

  • Srihera, Ramidha & Stute, Winfried, 2010. "Nonparametric comparison of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2039-2059, October.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2039-2059
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    References listed on IDEAS

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    1. Koul, Hira L. & Yi, Tingting, 2006. "Goodness-of-fit testing in interval censoring case 1," Statistics & Probability Letters, Elsevier, vol. 76(7), pages 709-718, April.
    2. Scheike, Thomas H., 2000. "Comparison of non-parametric regression functions through their cumulatives," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 21-32, January.
    3. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
    4. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    5. Gørgens, Tue, 2002. "Nonparametric comparison of regression curves by local linear fitting," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 81-89, November.
    6. King, Eileen & Hart, Jeffrey D. & Wehrly, Thomas E., 1991. "Testing the equality of two regression curves using linear smoothers," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 239-247, September.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Juan Carlos Pardo-Fernández & María Dolores Jiménez-Gamero & Anouar El Ghouch, 2015. "A Non-parametric ANOVA-type Test for Regression Curves Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 197-213, March.
    3. 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.

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