Deming Regression - Specification

Specification

Assume that the available data (y_i, x_i) are mismeasured observations of the “true” values (y_i*, x_i*):

$\begin{align} y_i &= y^*_i + \varepsilon_i, \\ x_i &= x^*_i + \eta_i, \end{align}$

where errors ε and η are independent and the ratio of their variances is assumed to be known:

In practice the variance of the and parameters is often unknown which complicates the estimate of but where the measurement method for and is the same they are likely to be equal so that for this case.

We seek to find the line of “best fit” y* = β₀ + β₁x*, such that the weighted sum of squared residuals of the model is minimized:

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