Recursive estimation of the conditional geometric median in Hilbert spaces

DOI10.1214/12-EJS759zbMath1295.62080arXiv1204.3213OpenAlexW2964056992MaRDI QIDQ1950915

Hervé Cardot, Peggy Cénac, Pierre-André Zitt

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.3213

zbMATH Keywords

asymptotic normalitykernel regressioncentral limit theoremaveragingsequential estimationstochastic gradientrobust estimatorRobbins-MonroMallows-Wasserstein distanceonline data

Mathematics Subject Classification ID

Nonparametric robustness (62G35) Nonparametric estimation (62G05) Central limit and other weak theorems (60F05) Stochastic approximation (62L20)

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Uses Software

• R
• fda (R)
• KernSmooth

Cites Work

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• Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm
• Uniform consistency of a class of regression function estimators for Banach-space valued random variables
• A class of Wasserstein metrics for probability distributions
• Linear processes in function spaces. Theory and applications
• Longitudinal functional principal component analysis
• Convergence of functional \(k\)-nearest neighbor regression estimate with functional responses
• Kernel regression with functional response
• On the \(u\)\,th geometric conditional quantile
• Functional data analysis.
• Nonlinear functional models for functional responses in reproducing kernel hilbert spaces
• Revisiting R\'ev\'esz's stochastic approximation method for the estimation of a regression function
• How to apply the method of stochastic approximation in the non-parametric estimation of a regression function¹
• Regression Analysis for a Functional Response
• The multivariate L ₁ -median and associated data depth
• Linear functional regression: The case of fixed design and functional response
• Conditional Functional Principal Components Analysis