Statistical inference in partially-varying-coefficient single-index model. (English) Zbl 1206.62113
Summary: Consider a varying-coefficient single-index model which consists of two parts: the linear part with varying coefficients and the nonlinear part with a single-index structure, and are hence termed as varying-coefficient single-index models. This model includes many important regression models such as single-index models, partially linear single-index models, varying-coefficient model and varying-coefficient partially linear models as special examples. We mainly study estimating problems of the varying-coefficient vector, the nonparametric link function and the unknown parametric vector describing the single-index in the model. A stepwise approach is developed to obtain asymptotic normality estimators of the varying-coefficient vector and the parametric vector, and estimators of the nonparametric link function with a convergence rate. The consistent estimator of the structural error variance is also obtained. In addition, asymptotic pointwise confidence intervals and confidence regions are constructed for the varying coefficients and the parametric vector. The bandwidth selection problem is also considered. A simulation study is conducted to evaluate the proposed methods, and real data analysis is also used to illustrate our methods.
MSC:
| 62H12 | Estimation in multivariate analysis |
| 62G08 | Nonparametric regression and quantile regression |
| 62G20 | Asymptotic properties of nonparametric inference |
| 65C60 | Computational problems in statistics (MSC2010) |
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