Annals of Operations Research

, Volume 276, Issue 1–2, pp 331–347 | Cite as

Nonparametric additive beta regression for fractional response with application to body fat data

  • Kuangnan FangEmail author
  • Xinyan Fan
  • Wei Lan
  • Bingquan Wang
S.I.: Computational Biomedicine


Fractional data that are restricted in the standard unit interval (0, 1) with a highly skewed distribution are commonly encountered. Such data arise in various areas, such as economics, finance, and medicine, among others. One natural idea to model such data is to use the beta family due to its flexibility to accommodate various density shapes. In this paper, we propose a nonparametric additive beta regression model along with a variable selection procedure, where the mean response is related to covariates through the combination of unknown functions of covariates, which can be approximated on a B-spline basis. By using this approximation method, we transform the problem of variable selection into the problem of selecting the groups of coefficients in the expansion. Based on the penalized likelihood method for group variable selection, we successfully select the significant covariates. Moreover, the estimation and selection consistencies and the properties of the penalized estimators are established. The simulation studies demonstrate that the performance of our proposed method is quite good. Finally, we apply the proposed method to body fat data, and we obtain several important findings with satisfactory selection and prediction performance.


Nonparametric additive beta regression Fractional data Variable selection Group SCAD 



This study has been supported by National Natural Science Foundation of China (71471152) and Fundamental Research Funds for the Central Universities of China (20720181003, 20720171095).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Kuangnan Fang
    • 1
    • 3
    Email author
  • Xinyan Fan
    • 1
  • Wei Lan
    • 2
  • Bingquan Wang
    • 1
  1. 1.Department of statistics, School of EconomicsXiamen UniversityXiamenChina
  2. 2.Statistics School and Center of Statistical ResearchSouthwestern University of Finance and EconomicsXiamenChina
  3. 3.Data Mining Research CenterXiamen UniversityXiamenChina

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