Penalized Relative Error Estimation of a Partially Functional Linear Multiplicative Model

  • Tao Zhang
  • Yuan Huang
  • Qingzhao Zhang
  • Shuangge MaEmail author
  • S. Ejaz Ahmed
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Functional data become increasingly popular with the rapid technological development in data collection and storage. In this study, we consider both scalar and functional predictors for a positive scalar response under the partially linear multiplicative model. A loss function based on the relative errors is adopted, which provides a useful alternative to the classic methods such as the least squares. Penalization is used to detect the true structure of the model. The proposed method can not only identify the significant scalar variables but also select the basis functions (on which the functional variable is projected) that contribute the response. Both estimation and selection consistency properties are rigorously established. Simulation is conducted to investigate the finite sample performance of the proposed method. We analyze the Tecator data to demonstrate application of the proposed method.


Functional data Partially linear Multiplicative model Penalized strategies Prediction Simulation 



We thank the organizers for invitation. The study was partly supported by the Fundamental Research Funds for the Central Universities (20720171064), the National Natural Science Foundation of China (11561006, 11571340), Research Projects of Colleges and Universities in Guangxi (KY2015YB171), Open Fund Project of Guangxi Colleges and Universities Key Laboratory of Mathematics and Statistical Model (2016GXKLMS005), and National Bureau of Statistics of China (2016LD01). Ahmed research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tao Zhang
    • 1
  • Yuan Huang
    • 2
  • Qingzhao Zhang
    • 3
  • Shuangge Ma
    • 4
    • 5
    Email author
  • S. Ejaz Ahmed
    • 6
  1. 1.School of ScienceGuangxi University of Science and TechnologyLiuzhouChina
  2. 2.Department of BiostatisticsUniversity of IowaIowa CityUSA
  3. 3.School of Economics and the Wang Yanan Institute for Studies in EconomicsXiamen UniversityXiamenChina
  4. 4.Department of BiostatisticsYale UniversityNew HavenUSA
  5. 5.VA Cooperative Studies Program Coordinating CenterWest HavenUSA
  6. 6.Department of Mathematics and StatisticsBrock UniversitySt. CatharinesCanada

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