Professor Milan Stehlík obtained his PhD in 2003 at Comenius University, Bratislava, Slovakia, and he habilitated in Statistics in 2011 in Johannes Kepler University in Linz, Austria. During 1.3.2014-1.10.2015 he was Associate Professor at Universidad Técnica Federico Santa María, Chile. He has received Full Professorship in 2015 in University of
Valparaiso, Valparaiso, Chile. He was involved in several international projects and collaborations in Austria, Spain, Russia, Canada, Germany among others. Currently he works at the Linz Institute of Technology (LIT) and Institute of Applied Statistics, Johannes Kepler University Linz and at Institute of Statistics, University of Valparaíso, Chile. He does research in Probability Theory, Statistics, Mathematics and their Applications for Medicine, Ecology and Finance, with several specializations in the experimental design, extremes, exact testing, life data modelling and reliability theory. He is Principal Investigator of Innovative project LIT-2016-1-SEE-023 Title: Modeling complex dependencies: how to make strategic multicriterial decisions? and Chilean FONDECYT Regular Project 2015-2019, N1151441: “Statistical and mathematical modelling as a knowledge bridge between Society and Ecology Sustainability”. |

## On algebraic condence sets

*Abstract:*

Hartigan’s “typical value theorem” (1969) [3] is the basis for random subsampling, a resampling plan which uses group theory to construct condence intervals for the center of a symmetric distribution on a real line. Atkins and Sherman [1] derived a group-theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 to be sufficient to provide typical values for 0.

Nowadays, in the “Big Data” era, subsampling from a complex data can be viewed as a natural solution to the computational issues induced by the immoderate size of databases. Since ignoring the survey scheme can impede estimation by introducing a non-negligible bias, it might be helpful to derive statistics under symmetry (or other group action) constrain. While a plethora of analyzes has already been conducted to provide unbiased and efficient estimation of average quantiles, to our knowledge, such is not the case for phenomenons involving invariance under the action of a nite re ection group, e.g. the hyperoctahedral groups of Bn type. We have addressed this issue in Francis, Stehli

OLYMPUS DIGITAL CAMERAk and Wynn [2]. New possibilities for building proper subsampling and algebraic condence covers are given. Relation of the generating function for groups of Bn type to the generating function for the number partition of an integer into at most n distinct parts (see G.H. Hardy and S. Ramanujan [4]) will be given.

We acknowledge project FONDECYT Regular, No. 1151441 and LIT-2016-1-SEE-023.