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).
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Whang, Yoon-Jae, 2001. "Consistent specification testing for conditional moment restrictions," Economics Letters, Elsevier, vol. 71(3), pages 299-306, June.
- Donald W. K. Andrews, 1997.
"A Conditional Kolmogorov Test,"
Econometric Society, vol. 65(5), pages 1097-1128, September.
- Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
- 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.
- 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.
- 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.
- 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.
- 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.
- Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
- repec:adr:anecst:y:2006:i:81:p:02 is not listed on IDEAS
- Bierens, Herman J, 1990.
"A Consistent Conditional Moment Test of Functional Form,"
Econometric Society, vol. 58(6), pages 1443-58, 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.
- Lavergne, Pascal & Patilea, Valentin, 2008.
"Breaking the curse of dimensionality in nonparametric testing,"
Journal of Econometrics,
Elsevier, vol. 143(1), pages 103-122, March.
- Pascal Lavergne & Valentin Patilea, 2006. "Breaking the Curse of Dimensionality in Nonparametric Testing," Working Papers 2006-24, Centre de Recherche en Economie et Statistique.
- 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.
- 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.
- 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 1403-30, November.
- 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.
- 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.
- 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.
- Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
- 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.
- Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-81, November.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:143:y:2008:i:1:p:103-122. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.