Deviation probability bound for martingales with applications to statistical estimation
- Liptser, Robert
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62G05 62M99
- martingale, deviation probability, maximum likelihood estimate, autoregression, linear diffusion
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.
- Stat. and Prob. Letters, 46 (1999),pp. 357-374