The Computation and Use of the Asymptotic Covariance Matrix for Measurement Error Models (Classic Reprint) - Hardcover

Boggs, Paul T.

9780428943561: The Computation and Use of the Asymptotic Covariance Matrix for Measurement Error Models (Classic Reprint)

Hardcover

ISBN 10: 042894356X ISBN 13: 9780428943561

Verlag: Forgotten Books, 2018

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Excerpt from The Computation and Use of the Asymptotic Covariance Matrix for Measurement Error Models

This problem goes under various names, including errors in variables, generalized least squares, orthogonal distance regression, and measurement error models. We prefer measurement error models in deference to the book of Fuller [1987] that presents the definitive modern treatment of the problem. We also use the term orthogonal distance regression since, as we show in �2, it is a useful geometric description of the problem actually solved.

As in the ordinary least squares case, when using measurement error models one is frequently interested in constructing. Confidence regions and or confidence intervals for the model parameters. To this end, Fuller derives the asymptotic form of the covariance matrix-and uses it in several examples. It is well known, however, that for nonlinear models in general, and for measurement error models in particular, confidence regions and intervals constructed using the covariance matrix are only approximate.

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