  Differential Privacy (DP) provides an elegant mathematical framework for
defining a provable disclosure risk in the presence of arbitrary adversaries;
it guarantees that whether an individual is in a database or not, the results
of a DP procedure should be similar in terms of their probability distribution.
While DP mechanisms are provably effective in protecting privacy, they often
negatively impact the utility of the query responses, statistics and/or
analyses that come as outputs from these mechanisms. To address this problem,
we use ideas from the area of robust statistics which aims at reducing the
influence of outlying observations on statistical inference. Based on the
preliminary known links between differential privacy and robust statistics, we
modify the objective perturbation mechanism by making use of a new bounded
function and define a bounded M-Estimator with adequate statistical properties.
The resulting privacy mechanism, named "Perturbed M-Estimation", shows
important potential in terms of improved statistical utility of its outputs as
suggested by some preliminary results. These results consequently support the
need to further investigate the use of robust statistical tools for
differential privacy.
