FPCA-based estimation for generalized functional partially linear models

  • Ruiyuan Cao
  • Jiang DuEmail author
  • Jianjun Zhou
  • Tianfa Xie
Regular Article


In real data analysis, practitioners frequently come across the case that a discrete response will be related to both a function-valued random variable and a vector-value random variable as the predictor variables. In this paper, we consider the generalized functional partially linear models (GFPLM). The infinite slope function in the GFPLM is estimated by the principal component basis function approximations. Then, we consider the theoretical properties of the estimator obtained by maximizing the quasi likelihood function. The asymptotic normality of the estimator of the finite dimensional parameter and the rate of convergence of the estimator of the infinite dimensional slope function are established, respectively. We investigate the finite sample properties of the estimation procedure via Monte Carlo simulation studies and a real data analysis.


Generalized linear model Functional partially linear model Quasi likelihood Karhunen–Loève representation 

Mathematics Subject Classification

62G08 62G20 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Ruiyuan Cao
    • 1
  • Jiang Du
    • 1
    Email author
  • Jianjun Zhou
    • 2
  • Tianfa Xie
    • 1
  1. 1.College of Applied SciencesBeijing University of TechnologyBeijingChina
  2. 2.School of Mathematics and StatisticsYunnan UniversityKunmingChina

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