Does MCD estimator suffers from swamping effect? If there are multiple outliers in the data set, the Mahalanobis distance suffers from masking and swamping effects. In order to rectify this problem, robust estimation of location and scale, such as Minimum Covariance Determinant or Minimum Volume Ellipsoid has been implemented. I thought that these estimators do not affected by masking and swamping. 
Actually I have generated 60 observation from bivariate normal distribution plus 5 outliers, according to Tukey–Huber contamination model. I was expecting MCD to identify only 5, but surprisingly MCD identified 7, two observation more than the real number of outliers. What is responsible for that?
Please correct me if I understand wrong. Thanks in advance.
 A: Yes, it is certainly possible for the (Fast)MCD to suffer from swamping and masking effects. That said, I think the question is best approached quantitatively, rather than in absolutes.
Given contaminated data, the objective of every robust estimator is to find a fit of the parameters of your model as close as possible to the one you would have had without the outliers. In order to achieve that, we have to trade fit quality in the presence of outliers against fit quality in their absence.
For FastMCD, the target model is typically elliptical, so the objective is to  find a good fit, close to the MLE solution, of $(\mu,\varSigma)$ on clean data in a way that still insures an acceptable fit  on contaminated  data. The usual measure of distance between  $(\hat{\mu},\hat{\varSigma})$ and  $(\mu,\varSigma)$ for this problem is the bias measure $b(\hat{\varSigma},\varSigma)$, defined in [0].
Now to get to your original question, swamping and masking will increase
$b(\hat{\varSigma},\varSigma)$. For example, the classical
estimator of  covariance does not suffer from swamping in the
absence of outliers, so it gets low (good) values of $b(\hat{\varSigma},\varSigma)$ when there are no outliers. However, it takes only a handful of nasty outliers to cause it
to have very large  values of $b(\hat{\varSigma},\varSigma)$.
Here, (Fast-)MCD offers a less steep trade-off (slightly higher values
of $b(\hat{\varSigma},\varSigma)$ when there are no outliers versus
much lower values when there are some).

Edit:
We can illustrate this trade off by measuring the $b(\hat{\varSigma},\varSigma)$ of several shift and affine equivariant estimators of scatter in R on your settings.
Basically, I m going to generate bivariate datasets of size $n=60$, add 5 outliers to them and see how good various estimators are doing.
Since the estimators I will compare are shift and affine equivariant I can, wlog, set $\varSigma=I_2$ (the rank two identity matrix) and $\mu=0_2$ (a vector of 0 of length 2). Because of this, we also have that:
$$b(\hat{\varSigma},\varSigma)=\log\left(\frac{\lambda_1(\hat{\varSigma})}{\lambda_2(\hat{\varSigma})}\right)$$
($\lambda_p(A)$ denotes the p-eigenvalue of $A$).
I will generate outliers as realizations of $\mathcal{N}_2(d_2,I_2/100),d\in\mathbb{R}$. I use a small variance ($I_2/100$) here because it is known that concentrated outliers  are the most difficult ones for affine equivariant estimators [1]. As for the value of $d$, I will take several values in a range $(0,20)$. The resulting R code:
library("ICSNP")
library("robustbase")
library("rrcov")

n<-60
p<-2
e<-5
m<-10

set.seed(123)
x<-matrix(rnorm(n*p),nc=2)
z<-matrix(rnorm(e*p,0,1/100),nc=2)
d<-seq(0,20,l=m)
results<-matrix(NA,m,6)
e<-vector("list",6)
#bias measure when varsigma=I_p
fx01<-function(ll,e){
    A<-eigen(e[[ll]])$values
    log(max(A)/min(A))
}

for(i in 1:m){#i<-1
    w<-sweep(z,2,rep(d[i],p),FUN="+")
    X<-rbind(x,w)
    e[[1]]<-cov(X)
    e[[2]]<-covMcd(X,nsamp="best")$cov
 e[[3]]<-symm.huber(X)
 e[[4]]<-HR.Mest(X)$scatter
    e[[5]]<-CovMest(X)@cov
    e[[6]]<-CovMMest(X)@cov
    results[i,]<-c(lapply(1:length(e),fx01,e=e),recursive=TRUE)
}
matplot(d,results,type="l",lwd=2,lty=1,col=1:6,ylab="bias",xlab="Distance of outliers")
legend("topleft",lty=1,lwd=2,col=1:6,legend=c("Classical","FMCD","Huber","HRM","CovMest","CovMMest"))

The resulting plot:

As you can see, the classical estimator of covariance, though it never suffers from swamping effect (by definition) and does best when the data contains no outliers, is in fact the worst choice when the data contains outliers. In that situation, the Huber M estimator of covariance is somewhere in the middle and all the other estimators do better. The best overall in this experiment seems to be FMCD, despite the fact that it suffers from swamping effect. The results would have been different had the rate of contamination or the number of dimensions
been higher so it is always worth doing these numerical experiments.

*

*[0]: Yohai, V.J. and Maronna, R.A. (1990).
The Maximum Bias of Robust Covariances.
Communications in Statistics--Theory and Methods, 19, 3925--2933.

*[1] Rocke D. M. and  Woodruff D. L. (1996).
Identification of Outliers in Multivariate Data.
Journal of the American Statistical Association, 91, 1047--1061.

