A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function that satisfies a quasi-linear partial differential equation of the first order. The integration of the partial differential equation with the aid of differential geometry is discussed. Applications to generalized linear models, linear mixed-effects models, and a location-scale family are presented.

翻译：针对一般估计量的最大似然估计渐近偏差缩减方法被提出。该估计量实现为插件估计量，其中参数通过满足一阶拟线性偏微分方程的惩罚函数最大化惩罚似然。讨论了借助微分几何求解该偏微分方程的方法，并展示了在广义线性模型、线性混合效应模型及位置-尺度族中的应用。