Efficient estimation of smooth functionals in Gaussian shift models

DOI10.1214/20-AIHP1081zbMath1469.62430arXiv1810.02767OpenAlexW3136456578MaRDI QIDQ2041800

Mayya Zhilova, Vladimir I. Koltchinskii

Publication date: 23 July 2021

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.02767

zbMATH Keywords

bootstrapefficiencynormal approximationconcentration inequalitiessmooth functionalsGaussian shift modeleffective rank

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Functional data analysis (62R10) Random matrices (probabilistic aspects) (60B20) Nonparametric statistical resampling methods (62G09)

Related Items

Functional estimation in log-concave location families, Estimation of smooth functionals in normal models: bias reduction and asymptotic efficiency, Estimation of smooth functionals in high-dimensional models: bootstrap chains and Gaussian approximation

Uses Software

• fda (R)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On asymptotically optimal confidence regions and tests for high-dimensional models
• Concentration inequalities and moment bounds for sample covariance operators
• Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance
• Minimax quadratic estimation of a quadratic functional
• Nonquadratic estimators of a quadratic functional
• Sharp adaptive estimation of quadratic functionals
• Hankel operators in the perturbation theory of unitary and self-adjoint operators
• Geometrizing rates of convergence. II
• On estimation of the \(L_r\) norm of a regression function
• Efficient estimation of integral functionals of a density
• Estimation of integral functionals of a density
• Applications of the van Trees inequality: A Bayesian Cramér-Rao bound
• Statistical analysis of observations of increasing dimension. Transl. from the Russian
• Minimax estimation of linear and quadratic functionals on sparsity classes
• Efficient estimation of linear functionals of principal components
• On adaptive estimation of linear functionals
• Functional data analysis.
• Asymptotically efficient estimation of smooth functionals of covariance operators
• Perturbation of Linear Forms of Singular Vectors Under Gaussian Noise
• Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory
• Some Problems on Nonparametric Estimation in Gaussian White Noise
• Introduction to General Statistical Analysis
• On the Efficiency of a Class of Non-Parametric Estimates
• Learning Theory
• Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models
• On Necessary Conditions for Efficient Estimation of Functionals of a Nonparametric Signal in White Noise
• Introduction to nonparametric estimation