An exponential inequality for autoregressive processes in adaptive tracking

Bernard Bercu (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability

A wide range of literature concerning classical asymptotic properties for linear models with adaptive control is available, such as strong laws of large numbers or central limit theorems. Unfortunately, in contrast with the situation without control, it appears to be impossible to find sharp asymptotic or nonasymptotic properties such as large deviation principles or exponential inequalities. Our purpose is to provide a first step towards that direction by proving a very simple exponential inequality for the standard least squares estimator of the unknown parameter of Gaussian autoregressive process in adaptive tracking.

Domaines: Probabilités [math.PR]

Bernard Bercu. An exponential inequality for autoregressive processes in adaptive tracking. Journal of Systems Science and Complexity, 2007, 20 (2), pp.243-250. ⟨hal-00201623⟩