A tail inequality for suprema of unbounded empirical processes with applications to Markov chains. (English) Zbl 1190.60010

Adamczak, Radoslaw

Electron. J. Probab. 13, 1000-1034 (2008).

Summary: We present a tail inequality for suprema of empirical processes generated by variables with finite \(\psi_\alpha\) norms and apply it to some geometrically ergodic Markov chains to derive similar estimates for empirical processes of such chains, generated by bounded functions. We also obtain a bounded difference inequality for symmetric statistics of such Markov chains.

MSC:

60E15

Inequalities; stochastic orderings

Keywords:

concentration inequalities; empirical processes; Markov chains