[RsR] Can robust estimators outperform least squares in nonlinear regression for pure Gaussian noise?

[Eduardo Conceição]

Dear Matthias,

I'm not aware of any proof for the optimality of least squares with respect to median(|LS estimator - true parameter|). I just assumed it was since You (1999) used it in his simulation study.

The same behavior, although mitigated, is observed when using the common mean squared error (MSE) criterion as you can see in the attached figure. Therefore, it seems that in some, *but not all*, degree this a consequence of the robust efficiency criterion as you've pointed out.

Best regards,
Eduardo
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