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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

##### 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
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