We study the optimal design problem under second-order least squaresestimation which is known to outperform ordinary least squares estimation whenthe error distribution is asymmetric. First, a general approximate theory isdeveloped, taking due cognizance of the nonlinearity of the underlyinginformation matrix in the design measure. This yields necessary and sufficientconditions that a D- or A-optimal design measure must satisfy. The results arethen 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 alsoaddressed.
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