Online estimation of the asymptotic variance for averaged stochastic gradient algorithms

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,...

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Bibliographic Details
Published in:Journal of statistical planning and inference Vol. 203; pp. 1 - 19
Main Author: Godichon, Antoine
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2019
Elsevier
Subjects:
Asymptotic variance
Averaging
Central Limit Theorem
Statistics
Statistics Theory
Stochastic gradient algorithm
Averaging
Stochastic gradient algorithm
Central Limit Theorem
Asymptotic variance
ISSN:0378-3758, 1873-1171
Online Access:Get full text
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Summary: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. •The asymptotic normality of averaged stochastic gradient estimates is established.•A recursive estimate of the asymptotic variance is introduced.•Rates of convergence of the recursive estimate of the variance are established.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2019.01.001