A tail inequality for suprema of unbounded empirical processes with applications to Markov chains

Details A tail inequality for suprema of unbounded empirical processes with applications to Markov chains A tail inequality for suprema of unbounded empirical processes with applications to Markov chains

2007-09-19

arxiv.org/abs/0709.3110v2

Mathematics

Probability

The main result in the independent case slightly improved. The presentation changed. To appear in Electronic Journal of Probab

Scientific paper

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.

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