Computational Statistics

, Volume 33, Issue 2, pp 623–638 | Cite as

H-relative error estimation for multiplicative regression model with random effect

  • Zhanfeng Wang
  • Zhuojian Chen
  • Zimu Chen
Original Paper


Relative error approaches are more of concern compared to absolute error ones such as the least square and least absolute deviation, when it needs scale invariant of output variable, for example with analyzing stock and survival data. A relative error estimation procedure based on the h-likelihood is developed to avoid heavy and intractable integration for a multiplicative regression model with random effect. Statistical properties of the parameters and random effect in the model are studied. Numerical studies including simulation and real examples show the proposed estimation procedure performs well.


h-likelihood Laplace approximation Asymptotic property 



The authors are grateful to the Editor, the Associate Editor, and the anonymous referees for comments and suggestions that lead to improvements in the paper. This research is partially supported by funds of the State Key Program of National Natural Science of China (No. 11231010) and National Natural Science of China (No. 11471302).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics and Finance, Management SchoolUniversity of Science and Technology of ChinaHefeiChina

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