Abstract
We study depth measures for multivariate data defined by integrating univariate depth measures, specifically, integrated dual (ID) depth introduced by Cuevas and Fraiman (2009) which integrates univariate simplicial depth, and integrated rank-weighted (IRW) depth, which integrates univariate Tukey depth. We build on the results of Cuevas and Fraiman (2009) to show that IRW depth shares many depth properties with ID depth. Further, we provide additional results on exact computation, decreasing along rays, continuity and breakdown point that apply to both ID and IRW depth. We also establish asymptotic normality and consistency of the sample IRW depths. Lastly, we demonstrate the use of this depth measure with real and simulated datasets: calculating robust location estimators and dd-plots.
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