WIAS Preprint No. 3146, (2024)

Bernstein-type and Bennett-type inequalities for unbound matrix martingales


Authors

  • Kroshnin, Alexey
  • Suvorikova, Alexandra
    ORCID: 0000-0001-9115-7449

2020 Mathematics Subject Classification

  • 60E15

Keywords

  • Concentration, Bernstein inequality, Bennett inequality, martingales, Orlicz norm, empirical Bernstein, inequality, McDiarmid inequality

DOI

10.20347/WIAS.PREPRINT.3146

Abstract

We derive explicit Bernstein-type and Bennett-type concentration inequalities for matrix-valued supermartingale processes with unbounded observations. Specifically, we assume that the $psi_alpha$- Orlicz (quasi-)norms of their difference process are bounded for some $alpha > 0$. As corollaries, we prove an empirical version of Bernstein's inequality and an extension of the bounded differences inequality, also known as McDiarmid's inequality.

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