WIAS Preprint No. 371, (1997)

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.

Download Documents