The conditional expectation as estimator of normally distributed random variables with values in infinitely dimensional Banach spaces
type: Item
instance of: scholarly article
title: The conditional expectation as estimator of normally distributed random variables with values in infinitely dimensional Banach spaces
zbMATH Open document ID: 0732.62068
DOI: 10.1016/0047-259X(91)90028-Z
published in: Journal of Multivariate Analysis
publication date: 1991-01-01T00:00:00Z
review text: The present paper deals with an infinite-dimensional linear model \(\hat Z=Z_ 0(\hat f)+Y\) where \(\hat f: \Omega \to B_ 1\) and \(Y: \Omega \to B_ 2\) denote symmetric Gaussian random variables with values in separable Banach spaces \(B_ i\). Let \(Z_ 0 : B_ 1\to B_ 2\) denote a linear operator. Based on the observations \(\hat Z\) the author gives an explicit formula for the conditional expectation of \(\hat f\) given \(\hat Z\). This result is related to the generalized least squares estimator of \(\hat f\) to \(\hat Z\). Both expressions are asymptotically the same if Y is replaced by \(\sigma\) Y with \(\sigma \downarrow 0\). The result seems to be of some importance in nonparametrics.
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 4211307
zbMATH Keywords: infinite-dimensional linear model
zbMATH Keywords: symmetric Gaussian random variables
zbMATH Keywords: separable Banach spaces
zbMATH Keywords: linear operator
zbMATH Keywords: conditional expectation
zbMATH Keywords: generalized least squares estimator
author: Peter Krug
reviewed by: Arnold Janssen
MaRDI profile type: Publication
cites work: Q3254057
cites work: Q5533878
cites work: Q3938928
cites work: Q4162207
cites work: Q4148368
cites work: Q3041461
cites work: Q4052400
cites work: Q5583383
cites work: Q3870155
cites work: Construction of optimal designs in random coefficient regression models
description: scientific article; zbMATH DE number 4211307