Optimal two-stage procedures for estimating location and size of the maximum of a multivariate regression function

DOI10.1214/12-AOS1053zbMath1296.62158arXiv1302.4561OpenAlexW3100239388WikidataQ57429638 ScholiaQ57429638MaRDI QIDQ741809

Subhashis Ghosal, Harry van Zanten, Eduard Belitser

Publication date: 15 September 2014

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

Full work available at URL: https://arxiv.org/abs/1302.4561

zbMATH Keywords

adaptive estimationtwo-stage procedureoptimal ratesequential designmulti-stage procedure

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Nonparametric estimation (62G05) Sequential statistical design (62L05) Sequential estimation (62L12)

Related Items

Uniform convergence of local Fréchet regression with applications to locating extrema and time warping for metric space valued trajectories, Bayesian mode and maximum estimation and accelerated rates of contraction, Estimation and inference for minimizer and minimum of convex functions: optimality, adaptivity and uncertainty principles

Cites Work

• A two-stage hybrid procedure for estimating an inverse regression function
• Optimal order of accuracy of search algorithms in stochastic optimization
• Lower rate of convergence for locating a maximum of a function
• Nonparametric estimation of the location of a maximum in a response surface.
• Accelerated randomized stochastic optimization.
• Adaptive nonparametric peak estimation
• Least squares estimators of the mode of a unimodal regression function
• Change-point estimation under adaptive sampling
• A companion for the Kiefer-Wolfowitz-Blum stochastic approximation algorithm
• Adaptive estimation of the mode of a multivariate density
• Stochastic Estimation of the Maximum of a Regression Function
• Multidimensional Stochastic Approximation Methods
• Unnamed Item
• Unnamed Item
• Unnamed Item