On adaptive estimation in partial linear models
- Golubev, Georgi
- Härdle, Wolfgang
2010 Mathematics Subject Classification
- 62G05 62G20
- Adaptive estimation, second order minimax risk, penalized likelihood
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.