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

  • Manuel Wiesenfarth
  • Tatyana Krivobokova
  • Stephan Klasen
  • Stefan Sperlich

This 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 .

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File URL: http://hdl.handle.net/10.1080/01621459.2012.682809
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Article provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.

Volume (Year): 107 (2012)
Issue (Month): 500 (December)
Pages: 1286-1296

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Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1286-1296
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  1. John Maindonald, . "Generalized Additive Models: An Introduction with R," Journal of Statistical Software, American Statistical Association, vol. 16(b03).
  2. 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.
  3. Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
  4. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
  5. M. Ruth & K. Donaghy & P. Kirshen, 2006. "Introduction," Chapters, in: Regional Climate Change and Variability, chapter 1 Edward Elgar.
  6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
  7. 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.
  8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
  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. 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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