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Direct Simultaneous Inference in Additive Models and its Application to Model Undernutrition

  • Manuel Wiesenfarth

    (Georg-August-University Göttingen)

  • Tatyana Krivobokova

    (Georg-August-University Göttingen)

  • Stephan Klasen

    (Georg-August-University Göttingen)

  • Stefan Sperlich

    (Université de Genève)

This 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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Paper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 50.

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Date of creation: 07 Dec 2010
Date of revision: 21 Jul 2011
Handle: RePEc:got:gotcrc:050
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  1. Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
  2. Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
  3. Maindonald, John, 2006. "Generalized Additive Models: An Introduction with R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(b03).
  4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, December.
  5. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters, in: Regional Climate Change and Variability, chapter 1 Edward Elgar Publishing.
  6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, December.
  7. Sperlich, Stefan & Mammen, Enno & Huet, Sylvie & Hardle, Wolfgang, 2000. "Bootstrap inference in semiparametric generalized additive models," DES - Working Papers. Statistics and Econometrics. WS 10079, Universidad Carlos III de Madrid. Departamento de Estadística.
  8. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
  9. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
  10. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
  11. H rdle, Wolfgang & Huet, Sylvie & Mammen, Enno & Sperlich, Stefan, 2004. "Bootstrap Inference In Semiparametric Generalized Additive Models," Econometric Theory, Cambridge University Press, vol. 20(02), pages 265-300, April.
  12. 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.
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