Two‐stage model selection procedures in partially linear regression

The authors propose a two‐stage estimation procedure for the partially linear model Y = f_o(T) + X'β_o + ψ. They show how to estimate consistently the location of the nonzero components of β_o. Their approach turns out to be compatible with minimax adaptive estimation of f_o over Besov balls in the case of penalized least squares. Their proofs are based on a new type of oracle inequality.