Deming regression

Deming regression with the intercept constrained to zero

Deming regression is based on maximum likelihood estimation and it is used for fitting a line on measurement data when both X and Y have measurement errors. Implementations of Deming regression are available for the general case, but it is often required to fit a line whose intercept is constrained to zero. The function, DemingRegression, can perform both general Deming regression and the constrained fitting as well. It requires the measured data points (X and Y), the ratio of the variances of Y and X, and another input parameter which decides whether the intercept is to be constrained to zero.
Derivation of the general Deming model is available elsewhere (e.g. Wikipedia). A PDF showing the derivation of the equation for the slope if the intercept is zero is available in the submission.