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On multivariate quantile regression analysis

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  • Jean-Paul Chavas

    (University of Wisconsin)

Abstract

This paper investigates the estimation of parameters in a multivariate quantile regression model when the investigator wants to evaluate the associated distribution function. It proposes a new directional quantile estimator with the following properties: (1) it applies to an arbitrary number of random variables; (2) it is equivalent to estimating the distribution function allowing for non-convex distribution contours; (3) it satisfies nice equivariance properties; (4) it has desirable statistical properties (i.e., consistency and asymptotic normality); and (5) its implementation involves a modest computational burden: our proposed estimator can be obtained by solving parametric linear programming problems. As such, this paper expands the range of applications of quantile estimation for multivariate regression models.

Suggested Citation

  • Jean-Paul Chavas, 2018. "On multivariate quantile regression analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 365-384, August.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:3:d:10.1007_s10260-017-0407-x
    DOI: 10.1007/s10260-017-0407-x
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    References listed on IDEAS

    as
    1. Robert Serfling, 2010. "Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 915-936.
    2. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    3. Wei, Ying, 2008. "An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 397-409, March.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Alexander, Carol & Han, Yang & Meng, Xiaochun, 2023. "Static and dynamic models for multivariate distribution forecasts: Proper scoring rule tests of factor-quantile versus multivariate GARCH models," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1078-1096.
    2. Daouia, Abdelaati & Paindaveine, Davy, 2019. "Multivariate Expectiles, Expectile Depth and Multiple-Output Expectile Regression," TSE Working Papers 19-1022, Toulouse School of Economics (TSE), revised Feb 2023.
    3. Luca Merlo & Lea Petrella & Nikos Tzavidis, 2022. "Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's Strengths and Difficulties Questionnaire scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 417-448, March.

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    More about this item

    Keywords

    Multivariate; Quantile; Regression; Estimator; Nonconvex;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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