Asymptotic optimality and efficient computation of the leave-subject-out cross-validation

Ganggang Xu, Jianhua Z. Huang

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving the associated optimization problem is computationally expensive, especially when there are multiple tuning parameters. In this paper, by focusing on the penalized spline method, we show that the leave-subject-out CV is optimal in the sense that it is asymptotically equivalent to the empirical squared error loss function minimization. An efficient Newton-type algorithm is developed to compute the penalty parameters that optimize the CV criterion. Simulated and real data are used to demonstrate the effectiveness of the leave-subject-out CV in selecting both the penalty parameters and the working correlation matrix.

Original languageEnglish (US)
Pages (from-to)3003-3030
Number of pages28
JournalAnnals of Statistics
Issue number6
StatePublished - Dec 2012
Externally publishedYes


  • Cross-validation
  • Generalized estimating equations
  • Multiple smoothing parameters
  • Penalized splines
  • Working correlation matrices

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Asymptotic optimality and efficient computation of the leave-subject-out cross-validation'. Together they form a unique fingerprint.

Cite this