Weighted least squares and prediction
type: Item
instance of: scholarly article
title: Weighted least squares and prediction
zbMATH Open document ID: 0787.62091
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1993-01-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77440
review text: This paper introduces a weighted least-squares (WLS) method for estimation of the parameters in (pseudo) linear time-invariant regression models. It is proved that the WLS parameter estimator proposed behaves like the unweighted least-squares estimator in the usual parameter estimation case, and also that the former yields prediction errors having the properties of the prediction errors corresponding to the stochastic- gradient parameter estimator. The main tool of which is made use in the proofs is a weighted law of large numbers for vector-valued martingales. Owing to the bounds on quadratic means shown to hold true in the case of the WLS estimation, the solution to the adaptive tracking problem derived by using this estimator is shown, under weak conditions, to possess good properties such as consistency and almost-surely guaranteed convergence rates.
reviewed by: Petre Stoica
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 93E10
zbMATH DE Number: 97826
zbMATH Keywords: weighted least-squares
zbMATH Keywords: linear time-invariant regression models
zbMATH Keywords: WLS parameter estimator
zbMATH Keywords: prediction errors
zbMATH Keywords: stochastic-gradient parameter estimator
zbMATH Keywords: weighted law of large numbers for vector-valued martingales
zbMATH Keywords: bounds on quadratic means
zbMATH Keywords: adaptive tracking problem
zbMATH Keywords: consistency
zbMATH Keywords: almost-surely guaranteed convergence rates
author: Bernard Bercu
author: Marie Duflo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 97826