A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands was 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：本文主要讨论针对一般估算量的惯性偏差归纳优化问题，其估计方法是采用惩罚似然函数，通过对一阶拟线性分布方程的求解进行似然最大化。我们通过差分几何方法对这个部分微分方程进行积分计算。文章还探讨了该方法在广义线性模型、线性混合效应模型和位置-尺度族等多个模型中的应用。