Adaptive Estimation in High-Dimensional Response Surface Models via Iterative Thresholding Regularization

• Activity Number: 76
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Samir Touzani*+ and Anestis Antoniadis and Daniel Busby
• Companies: French Institut of Petroleum and University Joseph Fourier and French Institut of Petroleum
• Keywords: kernel estimation ; nonparametric regression ; Smoothing Spline ANOVA

Abstract

To perform the uncertainty analysis of computer experiments we model the outputs as nonparametric regression models with multivariate design points. Under the framework of Smoothing Spline ANOVA, we propose a new method based on L_{2} kernel estimation combined with L_{1} multidimensional regularization. The formulation of our estimator leads to an iterative thresholding algorithm which is designed to select a parsimonious model representation by selecting a small set of ANOVA terms. Numerical studies on simulated and real data, show that our method gives competitive performance compared to COSSO and some Gaussian processes approaches.