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Interquantile Shrinkage in Regression Models.

Liewen Jiang, Huixia Judy Wang, Howard D Bondell

    Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
    |December 24, 2013
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces novel penalization methods for quantile regression, improving estimation efficiency by jointly modeling multiple quantiles. These techniques detect and leverage commonalities in quantile coefficients for more accurate statistical analysis.

    Keywords:
    Fused lassoNon-crossingOracleQuantile regressionSmoothingSup-norm

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    Area of Science:

    • Statistics
    • Econometrics
    • Machine Learning

    Background:

    • Quantile regression traditionally analyzes quantiles separately.
    • Joint modeling can enhance estimation efficiency when quantile coefficients share common features.
    • Identifying interquantile commonality is crucial for robust statistical inference.

    Purpose of the Study:

    • To develop novel penalization methods for joint quantile regression analysis.
    • To automatically estimate and detect common features across quantile levels.
    • To improve the efficiency and accuracy of quantile regression models.

    Main Methods:

    • Development of two penalization techniques for joint quantile regression.
    • Estimation and detection of interquantile commonality in regression coefficients.
    • Theoretical establishment of oracle properties for the proposed methods.

    Main Results:

    • The proposed methods effectively shrink coefficients towards constancy when appropriate.
    • Demonstrated competitive or higher estimation efficiency compared to standard quantile regression.
    • Numerical investigations confirm the practical utility and performance of the new techniques.

    Conclusions:

    • Joint modeling with penalization offers significant advantages in quantile regression.
    • The developed methods provide a robust framework for analyzing interquantile commonality.
    • This approach enhances statistical efficiency and accuracy in diverse applications.