Statistical inference in partiallyvaryingcoefficient singleindex model 
 
Authors:  Qihua Wang Liugen Xue 
 
Institution:  ^{a} Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100080, China^{b} School of Mathematics and Statistics, Yunnan University, Kunming 650091, China^{c} College of Applied Sciences, Beijing University of Technology, Beijing 100022, China 
 
Abstract:  Consider a varyingcoefficient singleindex model which consists of two parts: the linear part with varying coefficients and the nonlinear part with a singleindex structure, and are hence termed as varyingcoefficient singleindex models. This model includes many important regression models such as singleindex models, partially linear singleindex models, varyingcoefficient model and varyingcoefficient partially linear models as special examples. In this paper, we mainly study estimating problems of the varyingcoefficient vector, the nonparametric link function and the unknown parametric vector describing the singleindex in the model. A stepwise approach is developed to obtain asymptotic normality estimators of the varyingcoefficient 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. 
 
Keywords:  62J99 62G20 
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