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

Abstract

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.

Keywords:

• Confidence band
• Heteroscedasticity
• Kenya
• Locally adaptive smoothing
• Penalized splines
• Specification test
• Varying variance

Acknowledgments

The authors acknowledge the support of the German Research Foundation (Deutsche Forschungsgemeinschaft) as part of the Institutional Strategy of the University of Göttingen. We also thank Jan Priebe for his help in processing the Kenyan data. The comments of the anonymous referees were very helpful in improving upon the first version of the article.