Optimal designs for regression models using the second-order least squares estimator

We investigate properties and numerical algorithms for Aand D-optimal regression designs based on the second-order least squares estimator (SLSE). Several theoretical results are derived, including an innovative expression to characterize the A-optimality criterion. We can formulate the optimal design problems under SLSE as semidefinite programming or convex optimization problems and show that the resulting algorithms can be faster than more conventional multiplicative algorithms, especially in nonlinear models. Our results also indicate that the optimal designs based on the SLSE are more efficient than those based on the ordinary least squares estimator, if the error distribution is highly skewed. Corresponding author, email: [email protected], phone: 250-721-7470. 1 Statistica Sinica: Newly accepted Paper (accepted version subject to English editing)