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Multivariate expectile trimming and the BExPlot

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  • Cascos Fernández, Ignacio
  • Ochoa Arellano, Maicol Jesús

Abstract

Expectiles are the solution to an asymmetric least squares minimization problem for univariate data. They resemble some similarities with the quantiles, and just like them, expectiles are indexed by a level α. In the present paper, we introduce and discuss the main properties of the expectile multivariate trimmed regions, a nested family of sets, whose instance with trimming level α is built up by all points whose univariate projections lie between the expectiles of levels α and 1 − α of the projected dataset. Such trimming level is interpreted as the degree of centrality of a point with respect to a multivariate distribution and therefore serves as a depth function. We study here the convergence of the sample expectile trimmed regions to the population ones and the uniform consistency of the sample expectile depth. We also provide efficient algorithms for determining the extreme points of the expectile regions as well as for computing the depth of a point in R2. These routines are based on circular sequence constructions. Finally, we present some real data examples for which the Bivariate Expectile Plot (BExPlot) is introduced.

Suggested Citation

  • Cascos Fernández, Ignacio & Ochoa Arellano, Maicol Jesús, 2019. "Multivariate expectile trimming and the BExPlot," DES - Working Papers. Statistics and Econometrics. WS 28434, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:28434
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    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Johanna F. Ziegel, 2016. "Coherence And Elicitability," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 901-918, October.
    3. Giorgi, Emanuele & McNeil, Alexander J., 2016. "On the computation of multivariate scenario sets for the skew-t and generalized hyperbolic families," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 205-220.
    4. Ruts, Ida & Rousseeuw, Peter J., 1996. "Computing depth contours of bivariate point clouds," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 153-168, November.
    5. Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
    6. Klaus Herrmann & Marius Hofert & Melina Mailhot, 2017. "Multivariate Geometric Expectiles," Papers 1704.01503, arXiv.org, revised Jan 2018.
    7. Breckling, Jens & Kokic, Philip & Lübke, Oliver, 2001. "A note on multivariate M-quantiles," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 39-44, November.
    8. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    9. Peter J. Rousseeuw & Ida Ruts, 1996. "Bivariate Location Depth," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 516-526, December.
    10. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
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