This paper deals with asymptotic robust properties of some estimators of scale parameter by the epsilon-contamination of the model distributions: F = Phi(epsilon,tau)(x) = (1 - epsilon) Phi (x) + epsilon Phi(x/tau), epsilon is a known proportion of contamination (0 < epsilon < 1 / 2), tau is a known scale parameter and Phi is the standard Gaussian distribution function. Assume that X-1,..., X-n is a random sample with distribution function F(x) and F has a density f (X), x is an element of R-1. Let T (F) F is an element of(sic), is a generic scale functional and T-n(X-1,..., X-n) = T(F-n) is its sample estimator. We consider the functional T (F) defined by integral[F(x +T(F))- F(x -T(F))- F(x)]dF(x) = 0 and the location invariance and scale equivariance sample estimators of the functional T (F) F is an element of (sic). The sample estimator of this functional T (F) is given by T-n (X-1,..., X-n) = med {vertical bar X-i - X-j vertical bar, 1 <= i, j <= n}. This estimator is also named as the median of the absolute differences. The purpose of this article is to study asymptotic robust properties T-n - estimators for different models distributions. The formal calculation of the Influence Function IF(x; F, T) is given by IF(x;F,T)= d(1)T(F;Delta(x) - F) = 1+ 2F(x - T)- 2F(x + T/2 integral[f(x + T) + f(x - T)]dF(x), x is an element of R-1. Note that Influence Function If (x; F, T) is bounded and looks like as the U-shaped curve. If [f (x +T)+ f (x - T)]dF (x) > 0, then the random variable root n{T-n - T(F)}/sigma(F, F-n) has asymptotically standard normal distribution, where the asymptotic variance of root nT(n) is given by the following formula: sigma(2) (F, T-n) = integral(infinity)(infinity) IF2 (x;F,T)dF(x) = f [1 +2F (x - T) - 2F (x +T)](2) dF (x)/4( [f (x +T) f (x -T)]c/F(x))(2). The paper contains numerical comparisons for some estimators of scale parameters by epsilon-contamination of the model distribution for different values of epsilon and tau. It is shown that for normal distribution asymptotic relative efficiency T-n - estimator with respect to S-1 having the classical standard deviation is equal: ARE(Phi) (T-n : S-1) = 0.86 and ARE(Phi) (T-n : S-2) = 0.98, where S-2 has the average absolute deviation.
