论文标题
一种强大而有效的算法，以查找轮廓似然置信区间
A robust and efficient algorithm to find profile likelihood confidence intervals
论文作者
论文摘要
如果未满足最大似然估计量的渐近性能，则轮廓似然置信区间是WALD方法的可靠替代方法。但是，在这些情况下，很难求解定义轮廓可能性置信区间的约束优化问题，因为可能性函数可能表现出不利的属性。结果，现有方法可能效率低下并产生误导性结果。在本文中，我们通过通过信任区域方法来计算轮廓的可能性置信区间来解决此问题，其中基于局部近似值计算的步骤限制在这些近似值足够精确的区域中。由于我们的算法也说明了如果可能性函数是强烈的线性或参数不可估计的，就会出现的数值问题，因此该方法适用于许多情况，在许多情况下，这些方法表明较早的方法被证明是不可靠的。为了证明其在应用中的潜力，我们将算法应用于基准问题，并将其与现有的6种方法进行比较，以计算概况概况可能的置信区间。我们的算法始终达到比任何竞争对手的成功率更高，同时也是最快的方法之一。由于我们的算法可以应用于参数和模型预测的两个置信区间，因此它在各种场景中很有用。
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood confidence intervals can be difficult to solve in these situations, because the likelihood function may exhibit unfavorable properties. As a result, existing methods may be inefficient and yield misleading results. In this paper, we address this problem by computing profile likelihood confidence intervals via a trust-region approach, where steps computed based on local approximations are constrained to regions where these approximations are sufficiently precise. As our algorithm also accounts for numerical issues arising if the likelihood function is strongly non-linear or parameters are not estimable, the method is applicable in many scenarios where earlier approaches are shown to be unreliable. To demonstrate its potential in applications, we apply our algorithm to benchmark problems and compare it with 6 existing approaches to compute profile likelihood confidence intervals. Our algorithm consistently achieved higher success rates than any competitor while also being among the quickest methods. As our algorithm can be applied to compute both confidence intervals of parameters and model predictions, it is useful in a wide range of scenarios.
