Séminaire MODAL'X : Azadeh Khaleghi (CREST, ENSAE)

Abstract: In this talk I will introduce some of our recent results on the estimation of mixing coefficients from stationary ergodic sample paths. Specifically, we have proposed strongly consistent estimators of the ℓ1 norm of the sequence of α-mixing (respectively β-mixing) coefficients of a stationary ergodic process. We have also provided strongly consistent estimators of individual α-mixing (respectively β-mixing) coefficients for a subclass of stationary α-mixing (respectively β-mixing) processes with summable sequences of mixing coefficients. The estimators are in turn used in the development of hypothesis tests for mixing rates. I will end with a discussion on the potential application of these results to the approximation of the optimal strategy in restless multi-armed bandits.