Le Breton, A.; Novikov, A. A. Averaging for estimating covariances in stochastic approximation. (English) Zbl 0826.60029 Math. Methods Stat. 3, No. 3, 244-266 (1994). Summary: Multidimensional linear stochastic approximation procedures in continuous time with Gaussian martingales as processes of errors are considered. Multistage algorithms are defined via averaging outputs of primary schemes with slowly varying gains. Under some general assumptions it is shown that these algorithms produce asymptotically optimal estimates. Moreover, based on a second order averaging, a strongly consistent procedure for estimating covariances of estimates is proposed. Cited in 1 ReviewCited in 3 Documents MSC: 60G15 Gaussian processes 62L20 Stochastic approximation 62G05 Nonparametric estimation Keywords:multidimensional linear stochastic approximation procedures; Gaussian martingales; strongly consistent procedure; estimating covariances PDFBibTeX XMLCite \textit{A. Le Breton} and \textit{A. A. Novikov}, Math. Methods Stat. 3, No. 3, 244--266 (1994; Zbl 0826.60029)