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On the predictive risk in misspecified quantile regression

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  • Giessing, Alexander
  • He, Xuming

Abstract

In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple (asymptotic) characterizations of the associated bias, also called expected optimism. We propose estimates for the expected optimism and the predictive risk, and establish their uniform consistency under mild conditions. Our results hold for models of moderately growing size and allow the quantile function to be incorrectly specified. Empirical evidence from our estimates is encouraging as it compares favorably with cross-validation.

Suggested Citation

  • Giessing, Alexander & He, Xuming, 2019. "On the predictive risk in misspecified quantile regression," Journal of Econometrics, Elsevier, vol. 213(1), pages 235-260.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:1:p:235-260
    DOI: 10.1016/j.jeconom.2019.04.013
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    Cited by:

    1. Chen, Zhao & Cheng, Vivian Xinyi & Liu, Xu, 2024. "Hypothesis testing on high dimensional quantile regression," Journal of Econometrics, Elsevier, vol. 238(1).
    2. Chen, Zhao & Cheng, Vivian Xinyi & Liu, Xu, 2024. "Reprint: Hypothesis testing on high dimensional quantile regression," Journal of Econometrics, Elsevier, vol. 239(2).

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    More about this item

    Keywords

    Quantile regression; Misspecification; Predictive risk; Expected optimism;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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