The limiting distribution of least squares in an errors-in-variables regression model
type: Item
instance of: scholarly article
title: The limiting distribution of least squares in an errors-in-variables regression model
zbMATH Open document ID: 0623.62015
author: Paul P. Gallo
author: Leon Jay Gleser
author: Raymond J. Carroll
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: The following regression model is considered: \[ y_ i=f'_{1i}\beta_ 1+f'_{2i}\beta_ 2+e_ i,\quad x_ i=f_{2i}+u_ i,\quad i=\quad 1,2,...,n. \] f\({}'_{1i}\) is a p-vector of observable predictors and \(f_{2i}\) is a q-vector of unobservable predictors. Moreover the errors \((u_ i\), \(e_ i)\) are independent and identically distributed with zero means. The unknown parameter \(\beta =(\beta_ 1\), \(\beta_ 2)\) is a \(p+q\)-vector and \({\hat \beta}\) is the ordinary least squares estimator. Some results concerning the consistency and the asymptotic normality of a linear combination, c'\({\hat \beta}\), are proven. Moreover, some special cases where \(f_{1i}\) and \(f_{2i}\) are fixed or random are studied.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 4011645
zbMATH Keywords: instrumental variables
zbMATH Keywords: functional models
zbMATH Keywords: structural models
zbMATH Keywords: observable predictors
zbMATH Keywords: unobservable predictors
zbMATH Keywords: ordinary least squares estimator
zbMATH Keywords: consistency
zbMATH Keywords: asymptotic normality
zbMATH Keywords: linear combination
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350262
OpenAlex ID: W2024947628
DOI: 10.1214/AOS/1176350262
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description: scientific article; zbMATH DE number 4011645