A general approach to the first order asymptotic analysis of penalized likelihood and related estimators is described. The method gives expansions for the systematic and random error. Asymptotic convergence rates in a family of spectral norms are obtained. The theory applies to a broad range of function estimation problems including nonparametric density, hazard and generalized regression curve estimation. Some examples are provided.
"Asymptotic Analysis of Penalized Likelihood and Related Estimators." Ann. Statist. 18 (4) 1676 - 1695, December, 1990. https://doi.org/10.1214/aos/1176347872