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Abstract
In this paper, the generalized varying-coefficient single-index model is discussed based on penalized likelihood. All the unknown functions are fitted by penalized spline. The estimates of the unknown parameters and the unknown coefficient functions are obtained and the estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. Two simulation studies are carried out to illustrate the performance of the estimates. An application of the model to the Hong Kong environmental data further demonstrates the potential of the proposed modelling procedures.
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Acknowledgements
We sincerely thank referees and associate editor for his/her valuable comments that lead to great improved presentation of our work.
The research was supported in part by National Natural Science Foundation of China [ 11171112,11101114 ], Doctoral Fund of Ministry of Education of China [ 20130076110004], Natural Science Project of Jiangsu Province Education Department [13KJB110024], Scientific Research Fund of Zhejiang Provincial Education Department [Y201121276 ] and National Statistical Science Research Major Program of China [ 2011LZ051 ].