  Extracting a common robust signal from data divided into heterogeneous groups
can be difficult when each group -- in addition to the signal -- can contain
large, unique variation components. Previously, maximin estimation has been
proposed as a robust estimation method in the presence of heterogeneous noise.
We propose soft maximin estimation as a computationally attractive alternative
aimed at striking a balance between pooled estimation and (hard) maximin
estimation.
  The soft maximin method provides a range of estimators, controlled by a
parameter $\zeta>0$, that interpolates pooled least squares estimation and
maximin estimation. By establishing relevant theoretical properties we argue
that the soft maximin method is both statistically sensibel and computationally
attractive.
  We also demonstrate, on real and simulated data, that the soft maximin
estimator can offer improvements over both pooled OLS and hard maximin in terms
of predictive performance and computational complexity.
  A time and memory efficient implementation is provided in the R package
\verb+SMME+ available on CRAN.
