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In case of robust estimators, What does Gaussian efficiency means? For example $Q_{_n}$ has 82% Gaussian efficiency and 50% breakdown point.

The reference is: Rousseeuw P.J., and Croux, C. (1993). “Alternatives to median absolute deviation.” J. American Statistical Assoc., 88, 1273-1283

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please add more context. Reference where you found this would be very helpful. – mpiktas May 6 '11 at 9:51
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My guess: If the sample follows a Gaussian distribution, then the asymptotic relative efficiency of the robust estimator in 95%. – cardinal May 6 '11 at 12:08
the reference is: Rousseeuw P.J., and Croux, C. (1993). “Alternatives to median absolute deviation.” J. American Statistical Assoc., 88, 1273-1283. – K-1 May 7 '11 at 4:51
@cardinal Your interpretation is almost always what is intended, especially in discussions of robust estimators. I would elevate your comment from "guess" to "near certainty." – whuber♦ May 17 '11 at 2:48
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@cardinal: your comment is the right answer. Please post it as so (i just saw this question). – user603 Jan 30 '12 at 7:02
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I guess Gaussian efficiency is something related to computation cost.

The efficiency of Gaussian adaptation relies on the theory of information due to Claude E. Shannon. When an event occurs with probability P, then the information −log(P) may be achieved. For instance, if the mean fitness is P, the information gained for each individual selected for survival will be −log(P) – on the average - and the work/time needed to get the information is proportional to 1/P. Thus, if efficiency, E, is defined as information divided by the work/time needed to get it we have: E = −P log(P). This function attains its maximum when P = 1/e = 0.37. The same result has been obtained by Gaines with a different method.

I may simply conclude that the higher the Gaussian Efficiency is, less resources (RAM) is needed for computing something like a robust scale estimator of a large sample. Since CPUs are much faster than the rest of computer we prefer to run a trial/error algorithm for times rather doing it at once with saying 128GB of RAM. when the Gaussian Efficiency is high the job will be done in a shorter time.

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This interpretation is sort of on the right track, at least at the beginning. I'm not sure who Gaines is or how it relates to this problem. But, see my hint, which provides you the answer. If needed, I can expand on it a bit. I would definitely not equate asymptotic relative efficiency to resources used, as you have tried to do in your last paragraph. – cardinal May 17 '11 at 2:17
@ Cardinal: Could you please explain more about Gaussian efficiency? For example what's the difference between Qn which benifits from 82% Gaussian efficiency and MAD with 37%? Actually my background is Coastal engineering far from statistics! – K-1 May 19 '11 at 7:13

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