Rate of convergence of truncated stochastic approximation procedures with moving bounds

Abstract

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix-valued random step-size sequence, and a dynamically changing random regression function. We study convergence and rate of convergence. Main results are supplemented with corollaries to establish various sets of sufficient conditions, with the main emphasis on the parametric statistical estimation. The theory is illustrated by examples and special cases.