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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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    2. Peter Pütz & Thomas Kneib, 2018. "A penalized spline estimator for fixed effects panel data models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 145-166, April.
    3. 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.
    4. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.
    5. 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.
    6. 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.
    7. 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).
    8. Benjamin Owusu & Bettina Bökemeier & Alfred Greiner, 2023. "Assessing nonlinearities and heterogeneity in debt sustainability analysis: a panel spline approach," Empirical Economics, Springer, vol. 64(3), pages 1315-1346, March.
    9. 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.
    10. Manuel Wiesenfarth & Carlos Matías Hisgen & Thomas Kneib & Carmen Cadarso-Suarez, 2014. "Bayesian Nonparametric Instrumental Variables Regression Based on Penalized Splines and Dirichlet Process Mixtures," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 468-482, July.
    11. K. De Brabanter & Y. Liu & C. Hua, 2016. "Convergence rates for uniform confidence intervals based on local polynomial regression estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 31-48, March.

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