Matrix parameter estimation in an autoregression model

Abstract

The vector difference equation ξk = Af(ξk−1)+εk, where (εk) is a square integrable difference martingale, is considered. A family of estimators ˇAn depending, besides the sample size n, on a bounded Lipschitz function is constructed. Convergence in distribution of √n (ˇAn − A) as n→∞is proved with the use of stochastic calculus. Ergodicity and even stationarity of (εk) is not assumed, so the limiting distribution may be, as the example shows, other than normal.