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Interpreting Expectiles

Author

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  • Collin Philipps

    (Department of Economics and Geosciences, US Air Force Academy)

Abstract

This article establishes how expectiles should be understood. An expectile is the minimizer of an asymmetric least squares criterion, making it a weighted average. This also means that an expectile is the conditional mean of the distribution under special circumstances. Specifically, an expectile of a distribution is a value that would be the mean if values above it were more likely to occur than they are. Expectiles summarize distributions in a manner comparable to quantiles, but quantiles are expectiles in location models. The reverse is true in special cases. Expectiles are m-estimators, m-quantiles, and Lp-quantiles, families which connect them to the majority of statistics commonly in use.

Suggested Citation

  • Collin Philipps, 2022. "Interpreting Expectiles," Working Papers 2022-01, Department of Economics and Geosciences, US Air Force Academy.
    • Handle: RePEc:ats:wpaper:wp2022-1
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    File URL: https://www.usafa.edu/app/uploads/usafawp2022-01.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Expectile regression; Generalized Quantile Regression;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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