Concentration Inequalities and Asymptotic Results for Ratio Type Empirical Processes

  title={Concentration Inequalities and Asymptotic Results for Ratio Type Empirical Processes},
  author={Evarist Gin{\'e} and Vladimir Koltchinskii},
where σP f ≥ Var P f and φ is a continuous, strictly increasing function with φ(0) = 0. Using Talagrand’s concentration inequality for empirical processes, we establish concentration inequalities for such suprema and use them to derive several results about their asymptotic behavior, expressing the conditions in terms of expectations of localized suprema of empirical processes. We also prove new bounds for expected values of sup-norms of empirical processes in terms of the largest σP f and the… CONTINUE READING
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