Asymptotically efficient estimation of smooth functionals of covariance operators

DOI10.4171/JEMS/1023zbMath1461.62068arXiv1710.09072OpenAlexW3102905895MaRDI QIDQ2659447

Vladimir I. Koltchinskii

Publication date: 26 March 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.09072

zbMATH Keywords

bootstrapperturbation theoryasymptotic efficiencynormal approximationconcentration inequalitiessample covarianceeffective rank

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Random matrices (probabilistic aspects) (60B20)

Related Items

Lower bounds for invariant statistical models with applications to principal component analysis, Efficient estimation of linear functionals of principal components, Functional estimation in log-concave location families, Dimension-free bounds for sums of independent matrices and simple tensors via the variational principle, Efficient estimation of smooth functionals in Gaussian shift models, Estimation of smooth functionals of location parameter in Gaussian and Poincaré random shift models., 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, Relative perturbation bounds with applications to empirical covariance operators

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