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