Skip to content

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

2 messages · Eduardo Conceicao, Matthias Kohl

Original
Eduardo Conceicao
# 
Hi,

I have recently conducted a Monte Carlo simulation study for robust univariate *nonlinear* regression estimators using small sample data taken from case studies in the chemical engineering field. The paper is available from doi:10.1016/j.compchemeng.2010.04.009

A very unusual finding was that for *pure* Gaussian error some of the robust estimators could *outperform* the least squares estimator. Even though I do not known of any theoretical result which prevents this behavior to happen, I have never seen it reported either.

I would like to known whether you find this acceptable or not and what you think might be causing it.

Thanks in advance for your help.

Eduardo L.T. Concei??o
Dept. of Chemical Engineering
University of Coimbra
Portugal
e-mail: econceicao at kanguru.pt; etc at eq.uc.pt
1 day later
Matthias Kohl
# 
Dear Eduardo,

I think a key point is the median-based efficiency criterion which you 
use to compare the estimators. In particular, do you know of a result 
which states that the least squares estimator is optimal with respect to 
median(|LS estimator - true parameter|)?

Beside that, I'm not convinced that this median-based efficiency 
criterion is a good choice for the comparison of estimators with the aim 
to investigate their robustness properties. But I will have a look at 
You (1999) in the next days.

Just my two cents.
Matthias
On 13.07.2010 05:45, Eduardo Concei??o wrote: