, i.e., its dimension is at least 7. This set a new record for real-world voting rules and the authors posed the exact … determination as a challenge. Recently, Chen et al. (An upper bound on the dimension of the voting system of the European Union … Council under the Lisbon rules, 2019, arXiv:1907.09711) showed that the dimension is at most 24. We provide the first improved …

This paper uses dimension asymptotics to study why overfit linear regression models shouldbe compared out-of-sample; we …

Most dimension reduction methods based on nonparametric smoothing are highlysensitive to outliers and to data coming …