Exponential inequalities for self-normalized martingales with applications

2007/07/31 by Bernard Bercu, Abderrahmen Touati · 105 citations
Computer Science · Decision Sciences · Mathematics · #Applied mathematics #Autoregressive model #Bayesian Methods and Mixture Models #Econometrics #Exponential function #Inequality #Mathematical analysis #Mathematical economics #Mathematics #Probability and Risk Models #Pure mathematics #Random variable #Statistics #Stochastic processes and statistical mechanics #math.PR #math.ST #msc:60E15 #msc:60G15 #msc:60G42 #msc:60J80 #stat.TH

paper · pdf · doi:10.1214/07-aap506

published in The Annals of Applied Probability 18(5) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/07-AAP506 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2008/10/01 · arxiv created 2008/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Peña. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated with linear regressions, autoregressive and branching processes are also provided.

Citations

• Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws
• Local limit theory and large deviations for supercritical Branching processes

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• Large deviation inequalities for martingales in Banach spaces
• Uniform convergence rates over maximal domains in structural\n nonparametric cointegrating regression