Simultaneous Confidence Bands for Additive Models with Locally Adaptive Smoothed Components and Heteroscedastic Errors

• Activity Number: 524
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Manuel Wiesenfarth*+ and Tatyana Krivobokova and Stephan Klasen
• Companies: Georg-August-Universitaet Goettingen and Georg-August-Universitaet Goettingen and Georg-August-Universitaet Goettingen
• Keywords: confidence band ; penalized splines ; volume-of-tube formula ; adaptive estimation ; mixed model ; nonparametric regression

Abstract

We propose a simple and fast approach to construct simultaneous confidence bands for smooth curves that enter an additive model, are spatially heterogeneous and are estimated from heteroscedastic data. Estimation is based on the mixed model representation of penalized splines which allows to fit such complex models from the corresponding likelihood and helps to build simultaneous confidence bands using the approximation to the tail probability of maxima of Gaussian processes. These confidence bands have very good small sample properties and are obtained instantly, i.e. without using bootstrap. Based on the resulted confidence bands a lack-of-fit test is proposed which not only performs competitively compared to likelihood ratio tests, but also allows to incorporate the above mentioned model features without any additional effort. Finite sample properties are studied in simulations and an application to undernutrition in Kenya shows the practical relevance of the approach. The method is implemented in the R package AdaptFitOS.