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Comparing two nonparametric regression curves in the presence of long memory in covariates and errors

Author

Listed:
  • Hira L. Koul

    (Michigan State University)

  • Fang Li

    (Indiana University Purdue University Indianapolis (IUPUI))

Abstract

This paper discusses the problem of testing the equality of two nonparametric regression functions against two-sided alternatives in the presence of long memory in the common covariate and errors. The proposed test is based on a marked empirical process of the differences between the response variables. We discuss asymptotic null distribution of this process and consistency of the test for a class of general alternatives. We also conduct a Monte Carlo simulation study to evaluate the finite sample level and power behavior of the test at some alternatives.

Suggested Citation

  • Hira L. Koul & Fang Li, 2020. "Comparing two nonparametric regression curves in the presence of long memory in covariates and errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 499-517, May.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:4:d:10.1007_s00184-019-00735-4
    DOI: 10.1007/s00184-019-00735-4
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    References listed on IDEAS

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    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: 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 442-447, September.
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    3. Ferreira, E. & Stute, W., 2004. "Testing for Differences Between Conditional Means in a Time Series Context," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 169-174, January.
    4. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameter for nonlinear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 211-251, March.
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    6. 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.
    7. Hira Koul & Donatas Surgailis & Nao Mimoto, 2015. "Minimum distance lack-of-fit tests under long memory errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 119-143, February.
    8. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    9. Härdle, W. & Marron, S.J., 1990. "Semiparametric comparison of regression curves," LIDAM Reprints CORE 890, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Koul, Hira L. & Baillie, Richard T. & Surgailis, Donatas, 2004. "Regression Model Fitting With A Long Memory Covariate Process," Econometric Theory, Cambridge University Press, vol. 20(3), pages 485-512, June.
    11. Javier Hidalgo & Peter M. Robinson, 2002. "Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory," Econometrica, Econometric Society, vol. 70(4), pages 1545-1581, July.
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    13. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
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