Expectile depth: Theory and computation for bivariate datasets

Abstract Expectiles are the solution to an asymmetric least squares minimization problem for univariate data. They resemble quantiles, and just like them, expectiles indexed by a level ? in unit interval. In present paper, we introduce discuss main properties of (multivariate) expectile regions, nested family sets, whose instance with 0 ? 1 ? 2 is built up all points projections lie between levels ? projected dataset. Such interpreted as degree centrality point respect multivariate distribution therefore serves depth function. We propose here algorithms determining extreme bivariate regions well computing plane. also study convergence sample population ones uniform consistency depth. Finally, some real data examples which Bivariate Expectile Plot (BExPlot) introduced.