Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method

arXiv:2404.07937v1 Announce Type: cross
Abstract: We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve the optimal rate for a wide range of problems, there have been no non-asymptotic results matching these optimal rates outside of a select few, typically linear, model classes. By leveraging modern tools from learning with dependent data, we provide the first …

abstract arxiv class cs.lg cs.sy eess.sy error least math.st parametric prediction rate squares stat.ml stat.th study type