# functional differences between using huber loss and winsorizing/trimming

Curious what the functional differences are between using a Huber loss function/ regression and Winsorizing data and then running a classic least squares regression.

Will the resulting outputs be roughly the same? Assuming no gross outliers? Are there situations in which one is preferred over the other?

• It's unclear how you are thinking of using Winsorizing in a least squares setting. Would you Winsorize the regressors, the response, both? Or would you Winsorize the residuals (effectively capping the quadratic loss) as part of the fitting algorithm? – whuber Jul 21 '17 at 15:40
• i was thinking mainly of winsorizing the regressors – Michael Jul 21 '17 at 17:35
• That would bias the results, perhaps strongly. What would be the point of it? Is it worth that price to mitigate the influence of some outlying regressor values? – whuber Jul 21 '17 at 17:40
• yes exactly - i thought it was a pretty standard process in statistical modeling – Michael Jul 21 '17 at 17:56
• Winsorizing is used in Exploratory Data Analysis to produce robust estimates of mean and variance of univariate datasets. I am unaware of (theoretically justified) applications of it in "statistical modeling" in general. – whuber Jul 21 '17 at 18:37

• Winsorizing that I have seen works on the extreme $p$% of observations, e.g. replacing the highest or lowest values by some value closer to the middle of the distribution. An M-estimate usually works in terms of the distance between a value and a reference level. For some simple cases, e.g. symmetrical unimodal distributions, a translation will be fairly simple, but not so far as I can see very helpful otherwise. – Nick Cox May 21 '19 at 23:47