Robust statistical comparison of random variables with locally varying scale of measurement

LANCASTER UNIVERSITY LEIPZIG

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Published

Standard

Robust statistical comparison of random variables with locally varying scale of measurement. / Jansen, Christoph; Schollmeyer, Georg; Blocher, Hannah et al.
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence. PMLR, 2023. (PMLR; Vol. 216).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Harvard

Jansen, C, Schollmeyer, G, Blocher, H, Rodemann, J & Augustin, T 2023, Robust statistical comparison of random variables with locally varying scale of measurement. in Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence. PMLR, vol. 216, PMLR. <https://proceedings.mlr.press/v216/jansen23a.html >

APA

Jansen, C., Schollmeyer, G., Blocher, H., Rodemann, J., & Augustin, T. (2023). Robust statistical comparison of random variables with locally varying scale of measurement. In Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence (PMLR; Vol. 216). PMLR. https://proceedings.mlr.press/v216/jansen23a.html

Vancouver

Jansen C, Schollmeyer G, Blocher H, Rodemann J, Augustin T. Robust statistical comparison of random variables with locally varying scale of measurement. In Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence. PMLR. 2023. (PMLR).

Author

Jansen, Christoph ; Schollmeyer, Georg ; Blocher, Hannah et al. / Robust statistical comparison of random variables with locally varying scale of measurement. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence. PMLR, 2023. (PMLR).

Bibtex

@inproceedings{307f2a3acfb8413b90e1fde9ad6a2019,

title = "Robust statistical comparison of random variables with locally varying scale of measurement",

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, or respectively perfect, cardinal structure is given. We derive a (regularized) statistical test for our proposed generalized stochastic dominance (GSD) order, operationalize it by linear optimization, and robustify it by imprecise probability models. Our findings are illustrated with data from multidimensional poverty measurement, finance, and medicine.",

author = "Christoph Jansen and Georg Schollmeyer and Hannah Blocher and Julian Rodemann and Thomas Augustin",

year = "2023",

month = jul,

day = "31",

language = "English",

series = "PMLR",

publisher = "PMLR",

booktitle = "Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence",

}

RIS

TY - GEN

T1 - Robust statistical comparison of random variables with locally varying scale of measurement

AU - Jansen, Christoph

AU - Schollmeyer, Georg

AU - Blocher, Hannah

AU - Rodemann, Julian

AU - Augustin, Thomas

PY - 2023/7/31

Y1 - 2023/7/31

N2 - 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, or respectively perfect, cardinal structure is given. We derive a (regularized) statistical test for our proposed generalized stochastic dominance (GSD) order, operationalize it by linear optimization, and robustify it by imprecise probability models. Our findings are illustrated with data from multidimensional poverty measurement, finance, and medicine.

AB - 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, or respectively perfect, cardinal structure is given. We derive a (regularized) statistical test for our proposed generalized stochastic dominance (GSD) order, operationalize it by linear optimization, and robustify it by imprecise probability models. Our findings are illustrated with data from multidimensional poverty measurement, finance, and medicine.

M3 - Conference contribution/Paper

T3 - PMLR

BT - Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence

PB - PMLR

ER -

Research

Links