Theory Informs Practice: Smoothing Parameters Selection for Smoothing Spline ANOVA Models in Large Samples

• Activity Number: 167 - Statistical Computing and Statistical Graphics: Student Paper Award and Chambers Statistical Software Award
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Xiaoxiao Sun* and Wenxuan Zhong and Ping Ma
• Companies: University of Georgia and University of Georgia and University of Georgia
• Keywords: smoothing splines ANOVA; smoothing parameters selection; generalized cross-validation; subsample

Abstract

Large samples have been generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyze such large samples due to expensive computational costs. In particular, the daunting computational costs of selecting smoothing parameters render the smoothing spline ANOVA models impractical. In this talk, I will present an asympirical (asymptotic + empirical) smoothing parameters selection approach for smoothing spline ANOVA models in large samples. The proposed method can significantly reduce computational costs of selecting smoothing parameters in high-dimensional and large-scale data. We show smoothing parameters chosen by the proposed method tend to the optimal smoothing parameters minimizing a risk function. In addition, the estimator based on the proposed smoothing parameters achieves the optimal convergence rate. Extensive simulation studies will be presented to demonstrate numerical advantages of our method over competing methods. I will further illustrate the empirical performance of the proposed approach using real data.