Deviation probability bound for martingales with applications to statistical estimation

R. Liptser*, V. Spokoiny

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let Mt be a vector martingale and 〈M〉t denote its predictable quadratic variation. In this paper we present a bound for the probability that z*〈M〉t-1M t>λz*〈M〉t -1z with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is non-asymptotic and does not require any ergodic assumption on the underlying model.

Original languageEnglish
Pages (from-to)347-357
Number of pages11
JournalStatistics and Probability Letters
Volume46
Issue number4
DOIs
StatePublished - 15 Feb 2000

Keywords

  • 62G05
  • Autoregression
  • Deviation probability
  • Linear diffusion
  • Martingale
  • Maximum likelihood estimate
  • Secondary 62M99

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