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

Radoslaw Adamczak (Polish Academy of Sciences)

Abstract


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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Pages: 1000-1034

Publication Date: June 29, 2008

DOI: 10.1214/EJP.v13-521

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