论文标题
超越三角洲方法
Beyond the delta method
论文作者
论文摘要
我们以涉及分数及其高阶导数的限制行为的方式，对最大似然估计器（MLE）或任何其他估计量进行渐近发展。这一开发是可以明确计算的，它提供了一些有关重新归一化MLE的非反应行为及其从极限偏离的见解。我们强调，每当分数及其衍生物收敛时，包括非高斯限制时，结果就会成立。我们的方法基于渐近隐式函数定理，灵感来自扰动方法。
We give an asymptotic development of the maximum likelihood estimator (MLE), or any other estimator defined implicitly, in a way which involves the limiting behavior of the score and its higher-order derivatives. This development, which is explicitly computable, gives some insights about the non-asymptotic behavior of the renormalized MLE and its departure from its limit. We highlight that the results hold whenever the score and its derivative converge, including to non Gaussian limits. Our approach is based on an asymptotic implicit function theorem, inspired from perturbative approaches.
