Econometrica: Jul 1987, Volume 55, Issue 4

Errors in Variables in Linear Systems

https://doi.org/0012-9682(198707)55:4<893:EIVILS>2.0.CO;2-9
p. 893-909

Edward E. Leamer

This paper extends the simple errors-in-variable bound to the setting of systems of equations. Both diagonal and nondiagonal measurement error covariance matrices are considered. In the nondiagonal case, the analogue of the simple errors-in-variable interval of estimates is an ellipsoid with diagonal equal to the line segment connecting the direct least squares with a two-stage least squares estimate. For the diagonal case, the set of estimates under some conditions must lie within the convex hull of 2^k points.

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