WIAS Preprint No. 471, (1999)

Deviation probability bound for martingales with applications to statistical estimation



Authors

  • Liptser, Robert
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62M99

Keywords

  • martingale, deviation probability, maximum likelihood estimate, autoregression, linear diffusion

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-1 Mt > λ√z* ⟨M⟩t-1 with a fixed vector z and discuss some 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.

Appeared in

  • Stat. and Prob. Letters, 46 (1999),pp. 357-374

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