Orthogonal Distance Regression ∗

Orthogonal Distance Regresson (ODR) is the name given to the computational problem associated with finding the maximum likelihood estimators of parameters in measurement error models in the case of normally distributed errors. We examine the stable and efficient algorithm of Boggs, Byrd and Schnabel (SIAM J. Sci. Stat. Comput., 8 (1987), pp. 1052– 1078) for finding the solution of this problem when the underlying model is assumed to be nonlinear in both the independent variable and the parameters. We also describe the associated public domain software package, ODRPACK. We then review the results of a simulation study that compares ODR with ordinary least squares (OLS). We also present the new results of an extension to this study. Finally we discuss the use of the asymptotic covariance matrix for computing confidence regions and intervals for the estimated parameters. Our conclusions are that ODR is better than OLS for the criteria considered, and that ODRPACK can provide effective solutions and useful statistical information for nonlinear ODR problems.

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