Asymptotic confidence regions of stochastic approximation procedures in Hilbert spaces

DOI10.1007/BF01046993zbMath0721.62080OpenAlexW2166925121MaRDI QIDQ2641050

Jürgen Dippon

Publication date: 1991

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01046993

zbMATH Keywords

separable Hilbert spacestopping rulesGaussian limit distributionRobbins-Monro methodasymptotic confidence ballscentered Gaussian random variablesDonsker type invariance principleestimator of the unknown radius of a ballrandom covariance operatorssequence of empirical covariance operators

Mathematics Subject Classification ID

Stochastic approximation (62L20) Optimal stopping in statistics (62L15)

Related Items (2)

Recursive estimation: asymptotic confidence regions by empirical quantiles ⋮ Parallel and bootstrapped stochastic approximation

Cites Work

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• An invariance principle for a finite dimensional stochastic approximation method in a Hilbert space
• Minimizing noisy functionals in Hilbert space: An extension of the Kiefer-Wolfowitz procedure
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• Martingales and the Robbins-Monro procedure in \(D[0,1\)]
• Bayesian inferences related to shifting sequences and two-phase regression
• Functional and random central limit theorems for the Robbins-Munro process
• On the Asymptotic Theory of Fixed-Size Sequential Confidence Bounds for Linear Regression Parameters
• On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean
• Fixed Size Confidence Ellipsoids for Linear Regression Parameters
• A limit theorem for the Robbins-Monro approximation

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