Deviation Inequalities for the Estimator of Linear Parameter in Stochastic Processes

Abstract

In this article, we obtain some deviation inequalities by non asymptotic approach, which extend the work of Liptser and Spokoiny (2000) in some sense, and apply them to the problem of the parameter estimation for more general regression models and Itô equations without any ergodic assumptions. In particular, for some special parameter estimation problems of discrete-time stochastic processes, we also give the more precise estimation.

Keywords:

• Deviation inequalities
• Estimating equation
• Linear model
• Optimal estimation

Mathematics Subject Classification:

• Primary 62F12
• Secondary 62M10

Acknowledgment

The authors are very grateful to the conscientious anonymous referee for his/her very serious and valuable comments.