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Breaking the curse of dimensionality in nonparametric testing

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  • Lavergne, Pascal
  • Patilea, Valentin

Abstract

For tests based on nonparametric methods, power crucially depends on the dimension of theconditioning variables, and specifically decreases with this dimension. This is known as the"curse of dimensionality." We propose a new general approach to nonparametric testing inhigh dimensional settings and we show how to implement it when testing for a parametricregression. The resulting test behaves against directional local alternatives almost as if thedimension of the regressors was one. It is also almost optimal against classes of onedimensionalalternatives for a suitable choice of the smoothing parameter. A simulationstudy shows that it outperforms the standard test by Zheng (1996).
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  • Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
    • Handle: RePEc:eee:econom:v:143:y:2008:i:1:p:103-122
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    as
    1. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1030-1051, December.
    2. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    3. repec:adr:anecst:y:2006:i:81:p:02 is not listed on IDEAS
    4. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    5. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    6. Hall, Peter & Yatchew, Adonis, 2005. "Unified approach to testing functional hypotheses in semiparametric contexts," Journal of Econometrics, Elsevier, vol. 127(2), pages 225-252, August.
    7. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
    8. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    9. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    10. Whang, Yoon-Jae, 2001. "Consistent specification testing for conditional moment restrictions," Economics Letters, Elsevier, vol. 71(3), pages 299-306, June.
    11. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    12. Guerre, Emmanuel & Lavergne, Pascal, 2002. "Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1139-1171, October.
    13. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    14. 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.
    15. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    16. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(4), pages 576-601, August.
    17. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    18. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
    19. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    20. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    21. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
    22. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August.
    23. Miguel A. Delgado & Manuel A. Dominguez & Pascal Lavergne, 2006. "Consistent Tests of Conditional Moment Restrictions," Annals of Economics and Statistics, GENES, issue 81, pages 33-67.
    24. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    25. Gozalo, Pedro L., 1997. "Nonparametric bootstrap analysis with applications to demographic effects in demand functions," Journal of Econometrics, Elsevier, vol. 81(2), pages 357-393, December.
    26. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 372-395, June.
    27. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    28. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
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    2. Katarzyna Bech & Grant Hillier, 2015. "Nonparametric testing for exogeneity with discrete regressors and instruments," CeMMAP working papers CWP11/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Pascal Lavergne & Valentin Patilea, 2011. "One for All and All for One: Regression Checks With Many Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 41-52, January.
    4. 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.
    5. Li, Lingzhu & Chiu, Sung Nok & Zhu, Lixing, 2019. "Model checking for regressions: An approach bridging between local smoothing and global smoothing methods," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 64-82.
    6. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.
    7. Chuanlong Xie & Lixing Zhu, 2018. "A minimum projected-distance test for parametric single-index Berkson models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 700-715, September.
    8. Christophe Bontemps & Jean‐Pierre Florens & Jean‐François Richard, 2008. "Parametric and Non‐parametric Encompassing Procedures," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 751-780, December.
    9. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    10. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    11. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
    12. Elia Lapenta & Pascal Lavergne, 2022. "Encompassing Tests for Nonparametric Regressions," Papers 2203.06685, arXiv.org, revised Oct 2023.
    13. Dai, Sheng, 2023. "Variable selection in convex quantile regression: L1-norm or L0-norm regularization?," European Journal of Operational Research, Elsevier, vol. 305(1), pages 338-355.
    14. Xie, Chuanlong & Zhu, Lixing, 2019. "A goodness-of-fit test for variable-adjusted models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 27-48.
    15. Chen, Feifei & Jiang, Qing & Feng, Zhenghui & Zhu, Lixing, 2020. "Model checks for functional linear regression models based on projected empirical processes," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    16. Sun, Zhihua & Chen, Feifei & Zhou, Xiaohua & Zhang, Qingzhao, 2017. "Improved model checking methods for parametric models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 147-161.
    17. Lapenta, Elia & Lavergne, Pascal, 2022. "Encompassing Tests for Nonparametric Regressions," TSE Working Papers 22-1332, Toulouse School of Economics (TSE).
    18. Junmin Liu & Deli Zhu & Luoyao Yu & Xuehu Zhu, 2023. "Specification testing of partially linear single-index models: a groupwise dimension reduction-based adaptive-to-model approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 232-262, March.
    19. Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.
    20. 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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