  We study the optimal design problem under second-order least squares
estimation which is known to outperform ordinary least squares estimation when
the error distribution is asymmetric. First, a general approximate theory is
developed, taking due cognizance of the nonlinearity of the underlying
information matrix in the design measure. This yields necessary and sufficient
conditions that a D- or A-optimal design measure must satisfy. The results are
then applied to find optimal design measures when the design points are binary.
The issue of reducing the support size of the optimal design measure is also
addressed.
