Robustfit for non-normal data

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.

Answer 1

[the cyclist]

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(...)

[JM90]

Many thanks for your assistance with this. I am most grateful for this clarification.

One further question related to normality, however, is whether the response (dependent variable) is required to be normally distributed. On the Matlab help for Robustfit it states "Default tuning constants give coefficient estimates that are approximately 95% as statistically efficient as the ordinary least-squares estimates, provided the response has a normal distribution with no outliers". Therefore, if the response (the variable to be predicted) is not normally distributed/has extreme data points, should this be subject to transformation before running the robust regression or is it acceptable to use the raw/untransformed data?

Again, many thanks for your assistance in advance.

[the cyclist]

That one I am not too sure about. I'd need to do some google searching, which it sounds like you'd be as qualified to do. :-)