New approach to distribution-free testing for Markov chains

About this event

Consider an empirical process, in any one of statistical contexts, and then apply unitary operator to this processes. Can one say what good could come out of this, and why will it be useful? The answer is that probably one can, as it leads us to a new point of view on distribution-free testing of probabilistic models. The specific answer in the case of parametric families of discrete distributions was described in 2013. For parametric empirical processes in $\R^d$ the approach was described in 2016. In this talk we will show two further examples: how can we have a theory of distribution-free tests for transition matrices of Markov chains, and, if we have time enough, and if my colleagues will find it of interest, how can we test regression model in the way, which does not depend on covariates