  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.
