Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,100
The problem of estimation of the finite dimensional parameter in a partial linear model is considered. We derive upper and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum likelihood estimator. It is well known that the performance of the estimator is depending on the choice of a smoothing parameter. We propose a practically feasible adaptive procedure for the penalization choice.
second order minimax risk Adaptive estimation penalized likelihood