Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement

arXiv:2306.12803v2 Announce Type: replace-cross
Abstract: Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to exploit the entire information encoded in them properly. We address this problem by considering an order based on (sets of) expectations of random variables mapping into such non-standard spaces. This order contains stochastic dominance and expectation order as extreme cases when no, …

abstract arxiv comparison cs.lg dimensions exploit information machine machine learning math.st measurement multidimensional question random robust scale spaces statistical statistics stat.ml stat.th them type variables