Bandwidth selection for nonparametric kernel testing
We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed-form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions. For example, when a significance level is given, we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level. Both asymptotic theory and methodology are established. In addition, we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example.
|Date of creation:||Dec 2005|
|Date of revision:||Jun 2007|
|Publication status:||Forthcoming in Journal of the American Statistical Association 4.483(2008): pp. 1-11|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
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.:
- Song Xi Chen & Wolfgang Härdle & Ming Li, 2003.
"An empirical likelihood goodness-of-fit test for time series,"
Journal of the Royal Statistical Society Series B,
Royal Statistical Society, vol. 65(3), pages 663-678.
- Chen, Song Xi & Härdle, Wolfgang & Kleinow, Torsten, 2000. "An empirical likelihood goodness-of-fit test for time series," SFB 373 Discussion Papers 2001,1, 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.
- Yacine Ait-Sahalia, 1995.
"Nonparametric Pricing of Interest Rate Derivative Securities,"
NBER Working Papers
5345, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
- Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
- Y. Nishiyama & Peter Robinson, 2004.
"The bootstrap and the Edgeworth correction for semiparametric averaged derivatives,"
CeMMAP working papers
CWP12/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 73(3), pages 903-948, 05.
- Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, 07.
- Manuel Arapis & Jiti Gao, 2006.
"Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 4(2), pages 310-345.
- Arapis, Manuel & Gao, Jiti, 2004. "Empirical comparisons in short-term interest rate models using nonparametric methods," MPRA Paper 11974, University Library of Munich, Germany, revised 23 Dec 2005.
- Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
- Holger Dette & Ingrid Spreckelsen, 2004. "Some comments on specification tests in nonparametric absolutely regular processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 159-172, 03.
- David A. Chapman & Neil D. Pearson, 1998.
"Is the Short Rate Drift Actually Nonlinear?,"
- Donald W. K. Andrews, 1997.
"A Conditional Kolmogorov Test,"
Econometric Society, vol. 65(5), pages 1097-1128, September.
- Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
- Yanqin Fan & Oliver Linton, 1997. "Some Higher Order Theory for a Consistent Nonparametric Model Specification Test," Cowles Foundation Discussion Papers 1148, Cowles Foundation for Research in Economics, Yale University.
- Zhang, Chunming & Dette, Holger, 2004. "A power comparison between nonparametric regression tests," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 289-301, February.
- Juhl, Ted & Xiao, Zhijie, 2005. "A nonparametric test for changing trends," Journal of Econometrics, Elsevier, vol. 127(2), pages 179-199, August.
- Gerhard Weihrather, 1993. "Testing a linear regression model against nonparametric alternatives," Metrika- International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 367-379, December.
- Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
- 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.
- W. González-Manteiga & R. Cao, 1993. "Testing the hypothesis of a general linear model using nonparametric regression estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 2(1), pages 161-188, December.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:11982. 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: (Joachim Winter)
If references are entirely missing, you can add them using this form.