Varying-coefficient single-index model. (English) Zbl 1452.62296
Summary: In this paper, the varying-coefficient single-index model (VCSIM) is proposed. It can be seen as a generalization of the semivarying-coefficient model by changing its constant coefficient part to a nonparametric component, or a generalization of the partially linear single-index model 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.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62-08 | Computational methods for problems pertaining to statistics |
Keywords:
asymptotic theory; average method; back-fitting technique; partially linear single-index model; local linear method; semivarying-coefficient modelSoftware:
KernSmoothReferences:
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