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

Author

Listed:
  • Manuel Wiesenfarth

    (Georg-August-University Göttingen)

  • Tatyana Krivobokova

    (Georg-August-University Göttingen)

  • Stephan Klasen

    (Georg-August-University Göttingen)

  • Stefan Sperlich

    (Université de Genève)

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:got:gotcrc:050
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, May.
    2. Maindonald, John, 2006. "Generalized Additive Models: An Introduction with R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(b03).
    3. Osmani, R.S., 1990. "Food Deprivation and Undernutrition in Rural Bangladesh," Research Paper 82, World Institute for Development Economics Research.
    4. 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.
    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. Haerdle,Wolfgang & Bowman,Adrian, 1986. "Bootstrapping in nonparametric regression: Local adaptive smoothing and confidence bands," Discussion Paper Serie A 71, University of Bonn, Germany.
    7. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
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    9. 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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    Citations

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    Cited by:

    1. Shuzhuan Zheng & Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2016. "Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 607-626, December.
    2. Rosales, Francisco & von-Cramon, Stephan, 2015. "Analysis of Price Transmission using a Nonparametric Error Correction Model with Time-Varying Cointegration," 2015 Conference, August 9-14, 2015, Milan, Italy 230227, International Association of Agricultural Economists.
    3. Stefan Sperlich, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 419-427, September.
    4. Peter Pütz & Thomas Kneib, 2016. "A Penalized Spline Estimator for Fixed Effects Panel Data Models," SOEPpapers on Multidisciplinary Panel Data Research 827, DIW Berlin, The German Socio-Economic Panel (SOEP).
    5. Umberto Amato & Anestis Antoniadis & Italia De Feis, 2016. "Additive model selection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 519-564, November.
    6. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.

    More about this item

    Keywords

    Additive model; Con dence band; Undernutrition; Heteroscedasticity; Locally adaptive smoothing; Kenya; Penalized splines; Varying variance;

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