Efficient penalized estimating method in the partially varying-coefficient single-index model

In this paper, penalized estimating equations are proposed to estimate the index parametric components, which is of primary interest, in the partially varying-coefficient single-index models (PVCSIMs). Although some procedures have been developed to estimate the index parameter in PVCSIM, the problem of how to conduct variable selection for the index in such models has not been addressed to date. To solve this problem, we propose a class of efficient penalized estimating equations, which combine the smoothly clipped absolute deviation (SCAD) penalty and a stepwise estimation method. The proposed method can simultaneously select significant variables in the index and estimate the nonzero smooth coefficient parameters. Under suitable conditions, we establish the theoretical properties of our penalized estimating procedure, including the oracle properties and the asymptotic normality for the resulting penalized estimation. We evaluate the performance of the proposed method by using Monte Carlo simulations and the application to a real dataset.