Estimation of smooth functionals of location parameter in Gaussian and Poincaré random shift models.
type: Item
instance of: scholarly article
title: Estimation of smooth functionals of location parameter in Gaussian and Poincaré random shift models.
zbMATH Open document ID: 1479.62035
author: M. Zhilova
author: Vladimir Koltchinskii
published in: Sankhyā. Series A
publication date: 2021-09-01T00:00:00Z
review text: The paper under review deals with the problem of estimating smooth functionals of location parameters in random noise models in Banach spaces. The authors study how the mean squared error rates in this problem depend on the smoothness of the functionals and determine how much smoothness is needed for efficient estimation. More specifically, they extend the results of [\textit{V. Koltchinskii} and \textit{M. Zhilova}, Ann. Inst. Henri Poincaré, Probab. Stat. 57, No. 1, 351--386 (2021; Zbl 1469.62430)] from Gaussian shift models to more general random shift models with noise having a distribution satisfying a Poincaré inequality (in particular, log-concave distribution). This is done both in the case of known noise distribution and also in the case when the distribution of the noise is Gaussian and the covariance is an unknown nuisance parameter.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 60B20
zbMATH DE Number: 7389300
zbMATH Keywords: smooth functionals
zbMATH Keywords: efficiency
zbMATH Keywords: random shift model
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: normal approximation
reviewed by: Joseph Melamed
MaRDI profile type: Publication
full work available at URL: s13171-020-00232-1
OpenAlex ID: W3118579919
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DOI: 10.1007/S13171-020-00232-1
description: scientific article; zbMATH DE number 7389300