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The limiting distribution of least squares in an errors-in-variables regression model. (English) Zbl 0623.62015
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

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
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