Concentration inequalities via zero bias couplings

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Goldstein L., IŞLAK Ü.

Statistics and Probability Letters, cilt.86, sa.1, ss.17-23, 2014 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 86 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.spl.2013.12.001
  • Dergi Adı: Statistics and Probability Letters
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.17-23
  • Anahtar Kelimeler: Primary, Stein's method, Tail probabilities, Zero bias coupling
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Boğaziçi Üniversitesi Adresli: Evet

Özet

The tails of the distribution of a mean zero, variance σ2 random variable Y satisfy concentration of measure inequalities of the form P(Y≥t) ≤ exp(-B(t)) for B(t)=t2/2(σ2 + ct) for t ≥ 0, and B(t)=t/c(log t -log log t-σ2/c)for t>e whenever there exists a zero biased coupling of Y bounded by c, under suitable conditions on the existence of the moment generating function of Y. These inequalities apply in cases where Y is not a function of independent variables, such as for the Hoeffding statistic Y=∑i=1naiπ(i) where A=(aij)1≤i,j≤n ∈Rn×n and the permutation π has the uniform distribution over the symmetric group, and when its distribution is constant on cycle type. © 2013 Elsevier B.V.