For a stable autoregressive process of order p with unknown vector parameter [theta], it is shown that under a sequential sampling scheme with the stopping time defined by the trace of the observed Fisher information matrix, the least-squares estimator of [theta] is asymptotically normally...

The paper deals with estimating problem of regression function at a given state point in nonparametric regression models with Gaussian noises and with non-Gaussian noises having unknown distribution. An asymptotically efficient kernel estimator is constructed for a minimax risk.

In this paper a concentration inequality is proved for the deviation in the ergodic theorem for diffusion processes in the case of discrete time observations. The proof is based on geometric ergodicity of diffusion processes. We consider as an application the nonparametric pointwise estimation...

We consider the deviation function in the ergodic theorem for an ergodic diffusion process (yt) where [phi] is some function, m([phi]) is the integral of [phi] with respect to the ergodic distribution of (yt). We prove a concentration inequality for [Delta]T([phi]) which is uniform with respect...