Semiparametric Additive Regression and Goodness-of-Fit

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ursula U. Müller*+
• Companies: Texas A&M University
• Keywords: Partly linear model ; nonparametric additive regression ; orthogonal series estimator ; uniform Bahadur representation

Abstract

We consider semiparametric additive regression models with a linear parametric part and a nonparametric part, both involving multivariate covariates. For the nonparametric part we assume that it is additive with smooth components. Our estimator of the regression curve is a suitable least squares approach involving series estimators. The resulting residual-based empirical distribution function can be used for goodness-of-fit tests, for example about the additivity assumption, or about the form of the error distribution. We show that the resulting residual-based empirical distribution function differs from the error-based empirical distribution function by an additive expression (up to a uniformly negligible remainder term). This result implies a functional central limit theorem.

This paper is based on joint work with Anton Schick and Wolfgang Wefelmeyer.