  It has previously been shown that ordinary least squares can be used to
estimate the coefficients of the single-index model under only mild conditions.
However, the estimator is non-robust leading to poor estimates for some models.
In this paper we propose a new sliced least-squares estimator that utilizes
ideas from Sliced Inverse Regression. Slices with problematic observations that
contribute to high variability in the estimator can easily be down-weighted to
robustify the procedure. The estimator is simple to implement and can result in
vast improvements for some models when compared to the usual least-squares
approach. While the estimator was initially conceived with the single-index
model in mind, we also show that multiple directions can be obtained, therefore
providing another notable advantage of using slicing with least squares.
Several simulation studies and a real data example are included, as well as
some comparisons with some other recent methods.
