  Nowadays, in many different fields, massive data are available and for
several reasons, it might be convenient to analyze just a subset of the data.
The application of the D-optimality criterion can be helpful to optimally
select a subsample of observations. However, it is well known that D-optimal
support points lie on the boundary of the design space and if they go hand in
hand with extreme response values, they can have a severe influence on the
estimated linear model (leverage points with high influence). To overcome this
problem, firstly, we propose an unsupervised exchange procedure that enables us
to select a nearly D-optimal subset of observations without high leverage
values. Then, we provide a supervised version of this exchange procedure, where
besides high leverage points also the outliers in the responses (that are not
associated to high leverage points) are avoided. This is possible because,
unlike other design situations, in subsampling from big datasets the response
values may be available.
  Finally, both the unsupervised and the supervised selection procedures are
generalized to I-optimality, with the goal of getting accurate predictions.
