Varying-coefficient single-index model

In this paper, the varying-coefficient single-indexmodel (VCSIM) is proposed. It can be seen as a generalization of the semivaryingcoefficient model by changing its constant coefficient part to a nonparametric component, or a generalization of the partially linear single-indexmodel by replacing the constant coefficients of its linear part with varying coefficients. Based on the local linear method, average method and backfitting technique, the estimates of the unknown parameters and the unknown functions of the VCSIM are obtained and their asymptotic distributions are derived. Both simulated and real data examples are given to illustrate the model and the proposed estimation methodology. © 2007 Elsevier B.V. All rights reserved. MSC: primary 62G08; secondary 62G20