Geometric View of Measurement Errors

What is it about?

We show that the slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of various slope estimators for the measurement error model including an adjusted fourth moment estimator introduced by Gillard and Iles (2005) to remove the jump discontinuity in the estimator of Copas (1972).

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Why is it important?

It is important in many experiments to recognize that the independent variable may not be free from errors. This paper illustrates the bias associated with different simple linear regression estimators and attempts to reduce bias by "smoothing" the estimator of Copas.