m-estimate for continuous values

Question

I'm building a custom regression tree and want to use m-estimate for pruning.

Does anyone know how to calculate that.

http://www.ailab.si/blaz/predavanja/UISP/slides/uisp07-RegTrees.ppt might help (slide 12, how should Em look like?)

Answer 1

There are a lot of m-estimates. They all boil down to recasting your estimation problem as a minimization problem. If you use squared error as the function you're minimizing, you just get sample mean. If you use absolute value of the error, you get the sample median. The idea is to use a function that is a compromise between these two so that you get some of the efficiency of the mean and some of the robustness of the median.

Once you've picked your function, finding an m-estimate is just an optimization problem. So your question really boils down to one of finding optimization software. If your optimization problem is convex (and you can pick your m-estimator so that the problem is convex) then there's a lot of high quality software out there.