Averaging analysis of a point process adaptive algorithm

Abstract

Motivated by a problem in neural encoding, we introduce an adaptive (or real-time) parameter estimation algorithm driven by a counting process. Despite the long history of adaptive algorithms, this kind of algorithm is relatively new. We develop a finite-time averaging analysis which is nonstandard partly because of the point process setting and partly because we have sought to avoid requiring mixing conditions. This is significant since mixing conditions often place restrictive history-dependent requirements on algorithm convergence.