Optimal designs for multi-factor nonlinear models based on the second-order least squares estimator

In this paper, we investigate the locally and maximin optimal design problems for multi-factor nonlinear models based on the second-order least squares estimator (SLSE), it is shown that the product-type designs are optimal based on the SLSE for the multi-factor nonlinear models without constant term when the sufficient conditions are satisfied. Some examples are presented to illustrate the theoretical results. Several by-products on locally and maximin optimal designs for uni-factor exponential decay models are also obtained.