A note on the generalized degrees of freedom under the L1 loss function

Xiaoli Gao, Yixin Fang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Generalized degrees of freedom measure the complexity of a modeling procedure; a modeling procedure is a combination of model selection and model fitting. In this manuscript, we consider two definitions of generalized degrees of freedom for a modeling procedure under the L1 loss function, and investigate the connections between those two definitions. We also propose the extended Akaike information criterion, the adaptive model selection, and the extended generalized cross-validation under the L1 loss function. Finally, we extend the results to M-estimation.

Original languageEnglish (US)
Pages (from-to)677-686
Number of pages10
JournalJournal of Statistical Planning and Inference
Issue number2
StatePublished - Feb 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Adaptive model selection
  • Covariance penalty
  • Degrees of freedom
  • Generalized cross-validation
  • Least absolute deviations
  • Modeling procedure


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