Resources & Economic Trade Department, Zhengzhou Institute of Aeronautical Industry Management,, Institute of electronic technology, The
PLA Information Engineering University, College of Applied Sciences, Beijing University of Technology

Partially linear model is a class of commonly
used semiparametric models, this paper focus on variable selection
and parameter estimation for partially linear models via adaptive
LASSO method. Firstly, based on profile least squares and adaptive
LASSO method, the adaptive LASSO estimator for partially linear
models are constructed, and the selections of penalty parameter and
bandwidth are discussed. Under some regular conditions, the
consistency and asymptotic normality for the estimator are
investigated, and it is proved that the adaptive LASSO estimator has
the oracle properties. The proposed method can be easily
implemented. Finally a Monte Carlo simulation study is conducted to
assess the finite sample performance of the proposed variable
selection procedure, results show the adaptive LASSO estimator
behaves well.