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Deviation probability bound for martingales with applications to statistical estimation

Author

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  • Liptser, R.
  • Spokoiny, V.

Abstract

Let Mt be a vector martingale and t denote its predictable quadratic variation. In this paper we present a bound for the probability that 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.

Suggested Citation

  • Liptser, R. & Spokoiny, V., 2000. "Deviation probability bound for martingales with applications to statistical estimation," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 347-357, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:4:p:347-357
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    Cited by:

    1. Dzhaparidze, K. & van Zanten, J. H., 2001. "On Bernstein-type inequalities for martingales," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 109-117, May.
    2. Saussereau, Bruno, 2012. "Deviation probability bounds for fractional martingales and related remarks," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1610-1618.

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