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An invariance principle for a finite dimensional stochastic approximation method in a Hilbert space

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  • Nixdorf, Rainer

Abstract

For the application of the classical Robbins-Monro procedure in a Hilbert space the statistician generally has to observe infinite dimensional vectors. A modified procedure is proposed, which works in appropriate finite dimensional subspaces of growing dimension. For this procedure an invariance principle is given together with some applications.

Suggested Citation

  • Nixdorf, Rainer, 1984. "An invariance principle for a finite dimensional stochastic approximation method in a Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 252-260, October.
    • Handle: RePEc:eee:jmvana:v:15:y:1984:i:2:p:252-260
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    Cited by:

    1. Chen Xiaohong & White Halbert, 2002. "Asymptotic Properties of Some Projection-based Robbins-Monro Procedures in a Hilbert Space," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-55, April.
    2. Caroline Geiersbach & Teresa Scarinci, 2021. "Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 78(3), pages 705-740, April.

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