Minimax filtration of linear transformations of stationary sequences
type: Item
instance of: scholarly article
title: Minimax filtration of linear transformations of stationary sequences
zbMATH Open document ID: 0727.62091
DOI: 10.1007/BF01066907
published in: Ukrainian Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: A linear least squares estimation problem is considered for the transformation \(A\xi =\sum^{\infty}_{j=0}a(j)\xi (-j)\) of a stationary stochastic sequence \(\xi\) (j) with spectral density f(\(\lambda\)) using observations of \(\xi (j)+\eta (j)\), \(j\leq 0\), where \(\eta\) (j) is a stationary sequence with spectral density g(\(\lambda\)). Least favourable spectral densities \(f_ 0(\lambda)\in {\mathcal D}_ f\), \(g_ 0(\lambda)\in {\mathcal D}_ g\), and minimax (robust) spectral characteristics of the optimal estimator of \(A\xi\) are found for different classes of spectral densities.
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60G25
Mathematics Subject Classification ID: 93E10
zbMATH DE Number: 4201435
zbMATH Keywords: minimax filtration
zbMATH Keywords: linear transformations of stationary sequences
zbMATH Keywords: filtering
zbMATH Keywords: linear least squares estimation
zbMATH Keywords: spectral density
zbMATH Keywords: Least favourable spectral densities
zbMATH Keywords: robust
zbMATH Keywords: optimal estimator
author: M. P. Moklyachuk
reviewed by: M. P. Moklyachuk
MaRDI profile type: Publication
cites work: Q5342183
cites work: Robust techniques for signal processing: A survey
cites work: Minimax-robust prediction of discrete time series
cites work: Q3951928
cites work: Sufficient conditions for extremum, penalty functions and regularity
full work available at URL: https://doi.org/10.1007/bf01066907
OpenAlex ID: W2076401806
description: scientific article; zbMATH DE number 4201435