Online estimation of the geometric median in Hilbert spaces: nonasymptotic confidence balls

DOI10.1214/16-AOS1460zbMath1371.62027arXiv1501.06930OpenAlexW4301224720MaRDI QIDQ2012199

Peggy Cénac, Antoine Godichon-Baggioni, Hervé Cardot

Publication date: 28 July 2017

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.06930

zbMATH Keywords

robust statistics functional data analysis recursive estimation spatial median stochastic gradient algorithms martingales in Hilbert spaces

Mathematics Subject Classification ID

Nonparametric robustness (62G35) Nonparametric estimation (62G05) Nonparametric tolerance and confidence regions (62G15) Stochastic approximation (62L20)

Related Items (20)

L^p and almost sure rates of convergence of averaged stochastic gradient algorithms: locally strongly convex objective ⋮ Multivariate \(\rho \)-quantiles: a spatial approach ⋮ Asymptotic properties of high-dimensional spatial median in elliptical distributions with application ⋮ On weighted multivariate sign functions ⋮ Optimal non-asymptotic analysis of the Ruppert-Polyak averaging stochastic algorithm ⋮ On the rates of convergence of parallelized averaged stochastic gradient algorithms ⋮ Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient ⋮ Spatial quantiles on the hypersphere ⋮ Volatility estimation in a nonlinear heteroscedastic functional regression model with martingale difference errors ⋮ Non asymptotic controls on a recursive superquantile approximation ⋮ Unnamed Item ⋮ Halfspace depths for scatter, concentration and shape matrices ⋮ Evaluating the complexity of some families of functional data ⋮ Fast estimation of the median covariation matrix with application to online robust principal components analysis ⋮ Algorithms of robust stochastic optimization based on mirror descent method ⋮ Stochastic approximation algorithms for superquantiles estimation ⋮ Online estimation of the asymptotic variance for averaged stochastic gradient algorithms ⋮ Conditional quantile sequential estimation for stochastic codes ⋮ Affine-equivariant inference for multivariate location under \({L_p}\) loss functions ⋮ On the Behavior of Extreme d-dimensional Spatial Quantiles Under Minimal Assumptions

This page was built for publication: Online estimation of the geometric median in Hilbert spaces: nonasymptotic confidence balls