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Multivariate quantiles with both overall and directional probability interpretation

Author

Listed:
  • Daniel Hlubinka
  • Lukáš Kotík
  • Miroslav Šiman

Abstract

The article introduces multivariate quantiles (or reference regions) that have both overall and directional probability interpretation and need not be necessarily convex. They are defined by means of univariate conditional quantiles along the rays starting at a suitable central point. Their basic properties are investigated, their sample estimators and regression extensions are proposed, and their use is illustrated with both simulated and real data.

Suggested Citation

  • Daniel Hlubinka & Lukáš Kotík & Miroslav Šiman, 2022. "Multivariate quantiles with both overall and directional probability interpretation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1586-1604, December.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:4:p:1586-1604
    DOI: 10.1111/sjos.12603
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    References listed on IDEAS

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