Direct Simultaneous Inference in Additive Models and its Application to Model Undernutrition
AbstractThis article proposes a simple and fast approach to build simultaneous confi dence 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 particular focus on the highly non-linear 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, i.e. without resampling methods. Finite sample properties of simultaneous con fidence bands and specifi cation tests are investigated in simulations. To facilitate and enhance its application, the method has been implemented in the R package AdaptFitOS.
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Bibliographic InfoPaper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 50.
Date of creation: 07 Dec 2010
Date of revision: 21 Jul 2011
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Additive model; Con dence band; Undernutrition; Heteroscedasticity; Locally adaptive smoothing; Kenya; Penalized splines; Varying variance;
Other versions of this item:
- Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2012. "Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition," Journal of the American Statistical Association, American Statistical Association, vol. 107(500), pages 1286-1296, December.
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- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
- 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.
- 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.
- Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
- 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.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
- Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
- 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.
- 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.
- Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
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