Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition
AbstractThis article proposes a simple and fast approach to build simultaneous confidence bands and perform specification tests for smooth curves in additive models. The method allows for handling of spatially heterogeneous functions and its derivatives as well as heteroscedasticity in the data. It is applied to study the determinants of chronic undernutrition of Kenyan children, with a particular focus on the highly nonlinear age pattern in undernutrition. Model estimation using the mixed model representation of penalized splines in combination with simultaneous probability calculations based on the volume-of-tube formula enable the simultaneous inference directly, that is, without resampling methods. Finite sample properties of simultaneous confidence bands and specification tests are investigated in simulations. To facilitate and enhance its application, the method has been implemented in the R package AdaptFitOS .
Download InfoIf 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.
Bibliographic InfoArticle provided by American Statistical Association in its journal Journal of the American Statistical Association.
Volume (Year): 107 (2012)
Issue (Month): 500 (December)
Contact details of provider:
Web page: http://www.amstat.org/publications/jasa/index.cfm?fuseaction=main
Other versions of this item:
- Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2010. "Direct Simultaneous Inference in Additive Models and its Application to Model Undernutrition," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 50, Courant Research Centre PEG, revised 21 Jul 2011.
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.:
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
- 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 9780521785167, November.
- John Maindonald, . "Generalized Additive Models: An Introduction with R," Journal of Statistical Software, American Statistical Association, vol. 16(b03).
- Jianqing Fan, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying-coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 27(4), pages 715-731.
- Claeskens, Gerda & Krivobokova, Tatyana & Opsomer, Jean, 2009. "Asymptotic properties of penalized spline estimators," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/211475, Katholieke Universiteit Leuven.
- Krivobokova, Tatyana & Kneib, Thomas & Claeskens, Gerda, 2010. "Simultaneous confidence bands for penalized spline estimators," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/255626, Katholieke Universiteit Leuven.
- Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 663-690, September.
- Krivobokova, Tatyana & Kneib, Thomas & Claeskens, Gerda, 2010. "Simultaneous confidence bands for penalized spline estimators," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/264495, Katholieke Universiteit Leuven.
- Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
- Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
- Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty).
If references are entirely missing, you can add them using this form.