Distributional hyperspace-convergence of Argmin-sets in convex -estimation

Research output: Contribution to journalResearch articleContributedpeer-review



In M-estimation we consider the sets of all minimizing points of convex empirical criterion functions. These sets are random closed sets. We derive distributional convergence in the hyperspace of all closed subsets of the real line endowed with the Fell-topology. As a special case single minimizing points converge in distribution in the classical sense. In contrast to the literature so far, unusual rates of convergence and non-normal limits emerge, which go far beyond the square-root asymptotic normality. Moreover, our theory can be applied to the sets of zero-estimators.


Original languageEnglish
Pages (from-to)3-35
Number of pages33
JournalTheory of probability and mathematical statistics
Early online dateOct 2023
Publication statusPublished - 2023

External IDs

WOS 001084577300001
Scopus 85163988294
Mendeley f2c6d3e9-6acc-3ecd-8e26-25106e194bc5



  • Argmin-sets, Fell-topology, M-estimation, Convex empirical processes, Random closed sets

Library keywords