Semiparametric variable selection for partially varying coefficient models with endogenous variables

By using instrumental variable technology and the partial group smoothly clipped absolute deviation penalty method, we propose a variable selection procedure for a class of partially varying coefficient models with endogenous variables. The proposed variable selection method can eliminate the influence of the endogenous variables. With appropriate selection of the tuning parameters, we establish the oracle property of this variable selection procedure. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.