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 with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is...</m>

We consider the possibility of optimal choice of observation window in the problem of parameter estimation by the observations of an inhomogeneous Poisson process. A minimax lower bound is proposed for the risk of estimation under an arbitrary choice of observation window. Then the adaptive...