Concentration inequalities using approximate zero bias couplings with applications to Hoeffding’s statistic under the Ewens distribution

  title={Concentration inequalities using approximate zero bias couplings with applications to Hoeffding’s statistic under the Ewens distribution},
  author={Nathakhun Wiroonsri},
  journal={Communications in Statistics - Theory and Methods},
  • Nathakhun Wiroonsri
  • Published 2 February 2022
  • Mathematics
  • Communications in Statistics - Theory and Methods
We prove concentration inequalities of the form P (Y ≥ t) ≤ exp(−B(t)) for a random variable Y with mean zero and variance σ using a coupling technique from Stein’s method that is so-called approximate zero bias couplings. Applications to the Hoeffding’s statistic where the random permutation has the Ewens distribution with parameter θ > 0 are also presented. A few simulation experiments are then provided to visualize the tail probability of the Hoeffding’s statistic and our bounds. Based on… 

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