  We analyse two classes of Einstein-Podolsky-Rosen (EPR)-steering
inequalities, the violation of which can be used to demonstrate EPR-steering
with an entangled two-qubit Werner state: linear inequalities and quadratic
inequalities. We discuss how post-selection of results (by appeal to the fair
sampling assumption) can compromise the rigour of these inequalities in
experimental tests of EPR-steering. By considering the worst-case scenarios in
which detector inefficiency or other loss could be exploited within a local
hidden-state model, we derive inequalities that enable rigorous but
loss-tolerant demonstrations of EPR-steering. The linear inequalities, and
special cases of the quadratic inequalities, have been used in recent
experiments. Our results indicate that regardless of the number of settings
used, quadratic inequalities are never better, and often worse, than linear
inequalities.
