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Asymptotic optimality of generalized cross validation and regularized Mallows model averaging

Author

Listed:
  • Zou, Chenchen
  • Li, Xin
  • Li, Xinmin
  • Liang, Hua

Abstract

We propose a modified generalized cross-validation model averaging procedure for weight choice and prove the asymptotic optimality of the resultant estimators in the squared loss sense under much weaker assumptions than those imposed in the literature. The proposed model averaging can be regarded as an L2-regularized Mallows model averaging with varying coefficients. Furthermore, we propose a GCV-adjusted Mallows model averaging that achieves a faster convergence rate towards the optimal loss compared to using generalized cross-validation model averaging or Mallows model averaging individually. The performance of the proposed estimators is thoroughly evaluated through numerical experiments.

Suggested Citation

  • Zou, Chenchen & Li, Xin & Li, Xinmin & Liang, Hua, 2025. "Asymptotic optimality of generalized cross validation and regularized Mallows model averaging," Statistics & Probability Letters, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:stapro:v:222:y:2025:i:c:s0167715225000513
    DOI: 10.1016/j.spl.2025.110406
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