The moderate deviation principle for minimizers of convex processes

Abstract

This paper mainly discusses the asymptotic behaviors on the minimizers of convex processes. In view of the convexity argument, it is proved that the minimizers of convex processes with parameterized objective functions satisfy the functional moderate deviation principle. As some applications, the estimators in two basic models (threshold regression models and stochastic dynamical systems) are studied. In particular, the exponential convergence principles on the estimators converging to true parameters are proved.