Penalized likelihood regression: general formulation and efficient approximation

The authors consider a formulation of penalized likelihood regression that is sufficiently general to cover canonical and noncanonical links for exponential families as well as accelerated life models with censored survival data. They present an asymptotic analysis of convergence rates to justify a simple approach to the lower-dimensional approximation of the estimates. Such an approximation allows for much faster numerical calculation, paving the way to the development of algorithms that scale well with large data sets.