A note on a maximal Bernstein inequality

A note on a maximal Bernstein inequality

We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.

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Veröffentlicht in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2011-08, Vol.17 (3), p.1054-1062
Hauptverfasser: KEVEI, PÉTER, MASON, DAVID M.
Format: Artikel
Sprache:eng
Schlagworte:
Bernstein inequality
Consistent estimators
Density estimation
dependent sums
Estimators
Induction assumption
Integers
Logarithms
Mathematical moments
maximal inequality
mixing
Partial sums
Random variables
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Zusammenfassung:We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
ISSN:1350-7265
DOI:10.3150/10-BEJ304