An asymptotic and empirical smoothing parameters selection method for smoothing spline ANOVA models in large samples

Xiaoxiao Sun, Wenxuan Zhong, Ping Ma

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Large samples are generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyse such large samples because of high computational costs. In particular, the daunting computational cost of selecting smoothing parameters renders smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection method for smoothing spline ANOVA models in large samples. The idea of our approach is to use asymptotic analysis to show that the optimal smoothing parameter is a polynomial function of the sample size and an unknown constant. The unknown constant is then estimated through empirical subsample extrapolation. The proposed method significantly reduces the computational burden of selecting smoothing parameters in high-dimensional and large samples. We show that smoothing parameters chosen by the proposed method tend to the optimal smoothing parameters that minimize a specific risk function. In addition, the estimator based on the proposed smoothing parameters achieves the optimal convergence rate. Extensive simulation studies demonstrate the numerical advantage of the proposed method over competing methods in terms of relative efficacy and running time. In an application to molecular dynamics data containing nearly one million observations, the proposed method has the best prediction performance.

Original languageEnglish (US)
Pages (from-to)149-166
Number of pages18
JournalBiometrika
Volume108
Issue number1
DOIs
StatePublished - Mar 1 2021
Externally publishedYes

Keywords

  • Asymptotic analysis
  • Generalized cross-validation
  • Smoothing parameters selection
  • Smoothing spline ANOVA model
  • Subsample

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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