Gleser, Leon Jay; Carroll, Raymond J.; Gallo, Paul P. The limiting distribution of least squares in an errors-in-variables regression model. (English) Zbl 0623.62015 Ann. Stat. 15, 220-233 (1987). 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. Reviewer: J.-R.Mathieu Cited in 13 Documents MSC: 62E20 Asymptotic distribution theory in statistics 62J05 Linear regression; mixed models 62F12 Asymptotic properties of parametric estimators 60F05 Central limit and other weak theorems 62H12 Estimation in multivariate analysis Keywords:instrumental variables; functional models; structural models; observable predictors; unobservable predictors; ordinary least squares estimator; consistency; asymptotic normality; linear combination PDFBibTeX XMLCite \textit{L. J. Gleser} et al., Ann. Stat. 15, 220--233 (1987; Zbl 0623.62015) Full Text: DOI