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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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File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_50.pdf
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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. 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.
  2. repec:cup:cbooks:9780521785167 is not listed on IDEAS
  3. John Maindonald, . "Generalized Additive Models: An Introduction with R," Journal of Statistical Software, American Statistical Association, vol. 16(b03).
  4. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters, in: Regional Climate Change and Variability, chapter 1 Edward Elgar.
  5. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
  6. 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.
  7. repec:cup:cbooks:9780521780506 is not listed on IDEAS
  8. Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
  9. Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
  10. 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.
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