Online estimation of the asymptotic variance for averaged stochastic\n gradient algorithms

Abstract

Stochastic gradient algorithms are more and more studied since they can deal\nefficiently and online with large samples in high dimensional spaces. In this\npaper, we first establish a Central Limit Theorem for these estimates as well\nas for their averaged version in general Hilbert spaces. Moreover, since having\nthe asymptotic normality of estimates is often unusable without an estimation\nof the asymptotic variance, we introduce a new recursive algorithm for\nestimating this last one, and we establish its almost sure rate of convergence\nas well as its rate of convergence in quadratic mean. Finally, two examples\nconsisting in estimating the parameters of the logistic regression and\nestimating geometric quantiles are given.\n