[RsR] Comparing M-estimators requires the same value of efficiency?

[Eduardo Conceicao]

Dear all,

In my field (chemical engineering) it is accepted in the literature that
comparing regression M-estimators *must* be done for the same value of
asymptotic efficiency.

However let us assume that for a particular instance  of a problem and for
some performance criterion:

- M-estimator A reaches the highest performance at 95% efficiency, and
- M-estimator B has the best performance at 80% efficiency.

I do not see any sense in comparing *both* the estimators at 80% or 95%.

Also, for some estimators of different kind, comparing at the same value
of efficiency would be impossible, for instance, an M-estimator and LMS
both at 95%.

Am I missing something here? Is there any theorem stating that different
M-estimators reach the best performance for the same asymptotic efficiency
in the same problem with the same performance criterion?

I would appreciate any comments that you may have.

Eduardo Conceicao
Sincerely