The univariate concept of quantile function---the inverse of a distribution function---plays a fundamental role in Probability and Statistics. In dimensions two and higher, however, inverting traditional distribution functions does not lead to any satisfactory notion. In their quest for an adequate concept of multivariate quantiles, statisticians developed two extremely fruitful theoretical pathways: copula transforms, where marginal quantiles are privileged over global ones, and depth functions, where a center-outward ordering is substituting the more traditional South-West/North-East one. None of these, unfortunately, induces a satisfactory concept of quantile function. We show how a recent center-outward definition, based on measure transportation ideas, of the concept of distribution function, yields notions of multivariate quantiles, ranks, and signs satisfying, in arbitrary dimension d, all the properties that make their univariate versions successful and vital tools of statistical inference.
The talk also can be joined online via our ZOOM MEETING
Meeting room opens at: June 19, 2023, 4.30 pm Vienna
Meeting ID: 688 0575 0235
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