Breaking the curse of dimensionality in nonparametric testing
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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- Juan Carlos Escanciano, 2005.
"A Consistent Diagnostic Test for Regression Models Using Projections,"
Faculty Working Papers
09/05, School of Economics and Business Administration, University of Navarra.
- Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1030-1051, December.
- 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.
- repec:adr:anecst:y:2006:i:81:p:02 is not listed on IDEAS
- Bierens, H.J. & Ploberger, W., 1995.
"Asymptotic theory of integrated conditional moment tests,"
1995-124, Tilburg University, Center for Economic Research.
- Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
- Donald W.K. Andrews, 1996.
"A Conditional Kolmogorov Test,"
Cowles Foundation Discussion Papers
1111R, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Lavergne, Pascal, 1998.
"An equality test across nonparametric regressions,"
SFB 373 Discussion Papers
1998,79, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
- 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.
- Whang, Yoon-Jae, 2001. "Consistent specification testing for conditional moment restrictions," Economics Letters, Elsevier, vol. 71(3), pages 299-306, June.
- Bierens, Herman J, 1990.
"A Consistent Conditional Moment Test of Functional Form,"
Econometric Society, vol. 58(6), pages 1443-1458, November.
- Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Guerre, Emmanuel & Lavergne, Pascal, 2002. "Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1139-1171, October.
- Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
- 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.
- Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
- Lavergne, Pascal & Vuong, Quang, 1998.
"Nonparametric significance testing,"
SFB 373 Discussion Papers
1998,75, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- 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.
- 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.
- Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
- Pascal Lavergne & Valentin Patilea, 2006.
"Breaking the Curse of Dimensionality in Nonparametric Testing,"
2006-24, Centre de Recherche en Economie et Statistique.
- Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
- 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.
- 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.
- 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.
- Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 372-395, June.
- 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.
- 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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