We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses.

中文翻译：

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基于最大拟似然估计量的优化设计

我们使用最优设计理论并基于最大拟似然估计量 (MqLE) 构建局部最优设计，该估计量是在比 MLE 方法所需条件更宽松的条件下导出的。我们表明，当误差分布来自指数族时，所提出的局部最优设计与基于 MLE 的设计渐进一样有效，并且它们的性能与基于任何其他渐近线性无偏估计量的最优设计一样好或更好，例如最小二乘估计 (LSE)。此外，我们展示了当前用于寻找最佳设计的算法可直接用于基于 MqLE 寻找最佳设计。作为一个说明性的应用程序，我们基于 MqLE 为 4 参数逻辑 (4PL) 模型构建了各种局部优化设计，并使用渐近相对效率研究了它们对模型中错误指定的鲁棒性特性。结果表明，基于 MqLE 的优化设计可以轻松生成，并且它们对于响应概率分布中的错误指定非常稳健。