# How to perform nonlinear regression on data with error?

Most of of physical measurements are associated with error, I am wondering how to perform nonlinear regression in this situation. In the linear case, there are few methods like Deming Regression, however, I have not seen any ref for nonlinear case. Just to put some context, assume we have a set of data $$(y_i+ey_i,x_i+ex_i)$$ where ex and ey are errors for our x and y measurements (not necessarily Gaussian). How do you take into account those error in the model? What is the best criteria to assess your model? Additionally, after you built your model, how do you predict for a given "x"? (I think you should take an average for prediction on [x-e,x+e] (e is error). I appreciate any reference.)

• What kind of nonlinear model do you mean, something like splines or polynomial regression. (Spoiler alert: both of those are linear.)
– Dave
Aug 19 at 16:23
• Well, not polynomial regression. The specific depends on the problem, it could be mixture of sinh/cosh (my current case), however, in general it could be any crazy function. I am trying to understand how to approach "nonlinear fitting in presence of error". I can not find any useful resources on the subject. Aug 19 at 20:35