A simple bootstrap method for constructing nonparametric confidence bands for functions
Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem, it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches and others based on nonstandard smoothing methods, complicate the process of inference, for example by requiring the choice of new, unconventional smoothing parameters and, in the case of undersmoothing, producing relatively wide bands. In this paper we suggest a new approach, which exploits to our advantage one of the difficulties that, in the past, has prevented an attractive solution to the problem— the fact that the standard bootstrap bias estimator suffer from relatively high-frequency stochastic error. The high frequency, together with a technique based on quantiles, can be exploited to dampen down the stochastic error term, leading to relatively narrow, simple-to-construct confidence bands. A supplement to this article, which outlines theoretical properties underpinning the methodology and provides a proof of theorem, can be viewed here
|Date of creation:||01 Jul 2013|
|Date of revision:|
|Contact details of provider:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Web page: http://cemmap.ifs.org.uk
More information through EDIRC
|Order Information:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
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.:
- H rdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004.
"Bootstrap Inference In Semiparametric Generalized Additive Models,"
Cambridge University Press, vol. 20(02), pages 265-300, April.
- Härdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2001. "Bootstrap Inference in Semiparametric Generalized Additive Models," Finance Working Papers 01-3, University of Aarhus, Aarhus School of Business, Department of Business Studies.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, December.
- Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
- 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.
- 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.
- Mendez, Guillermo & Lohr, Sharon, 2011. "Estimating residual variance in random forest regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2937-2950, November.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, December.
When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:29/13. 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: (Emma Hyman)
If references are entirely missing, you can add them using this form.