統計学輪講（第2回）

The main objective of this talk is to present bootstrap uniform functional central limit theorem for Harris recurrent Markov chains over uniformly bounded classes of functions. We show that the result can be generalized also to the unbounded case. To avoid some complicated mixing conditions, we make use of the well-known regeneration properties of Markov chains. We show that in the atomic case the proof of the bootstrap uniform central limit theorem for Markov chains for functions dominated by a function in L² space proposed by Radulovic (2004) can be significantly simplified. Regenerative properties of Markov chains can be applied in order to extend some concepts in robust statistics from i.i.d. to a Markovian setting. Bertail and Clemencon (2006) have defined an influence function and Frechet differentiability on the torus what allowed to extend the notion of robustness from single observations to the blocks of data instead. In this talk, we present bootstrap uniform central limit theorems for Frechet differentiable functionals in a Markovian case.