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Inference After Model Averaging In Linear Regression Models

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  • Zhang, Xinyu
  • Liu, Chu-An

Abstract

This article considers the problem of inference for nested least squares averaging estimators. We study the asymptotic behavior of the Mallows model averaging estimator (MMA; Hansen, 2007) and the jackknife model averaging estimator (JMA; Hansen and Racine, 2012) under the standard asymptotics with fixed parameters setup. We find that both MMA and JMA estimators asymptotically assign zero weight to the under-fitted models, and MMA and JMA weights of just-fitted and over-fitted models are asymptotically random. Building on the asymptotic behavior of model weights, we derive the asymptotic distributions of MMA and JMA estimators and propose a simulation-based confidence interval for the least squares averaging estimator. Monte Carlo simulations show that the coverage probabilities of proposed confidence intervals achieve the nominal level.

Suggested Citation

  • Zhang, Xinyu & Liu, Chu-An, 2019. "Inference After Model Averaging In Linear Regression Models," Econometric Theory, Cambridge University Press, vol. 35(4), pages 816-841, August.
    • Handle: RePEc:cup:etheor:v:35:y:2019:i:04:p:816-841_00
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    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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