MATLAB: Robustfit for non-normal data

robust regressionrobustfit

I am using robust fit for some non-normal data that has some extreme data points. A few queries. 1) For robust regression is it a requirement (like OLS) to have a normal distribution of residuals? I can see that the robustfit residuals differ slightly from OLS but they are very similar whichever tuning/weight function is utilised. 2) If not (Q1) how do I evaluate whether using robust fit has corrected for departures of normality/extreme data points?
Many thanks in advance.

Best Answer

It is not a requirement that residuals from a robust regression be normally distributed. On the contrary, robust regression techniques would typically be used only if outliers are violating the assumption of normally distributed residuals.
I'm not an expert on these techniques, but I guess that one way to get a handle on whether the robust fit is "doing what it claims to do" is by looking at how much the algorithm is down-weighting the outlier observations. You can see the observation weighting in the output stats.w when you call
[b,stats] = robustfit(...)
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