Statistics and Its Interface

Volume 10 (2017)

Number 3

Semiparametric hierarchical model with heteroscedasticity

Pages: 413 – 424



Chuoxin Ma (School of Mathematics, University of Manchester, United Kingdom)

Maozai Tian (Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China; and School of Statistics, Lanzhou University of Finance and Economics, Lanzhou, Gansu, China)

Jianxin Pan (School of Mathematics, University of Manchester, United Kingdom)


Recent work on hierarchical data analysis mainly focuses on the multilevel structure of the mean response. Little research for hierarchical heteroscedasticity was done in the literature. In this paper, we propose a class of hierarchical models with heteroscedasticity and then investigate the semi-parametric statistical inferences. Laplace’s approximation is employed to obtain an approximated marginal likelihood function and splines method is used to estimate the unknown functions. We also provide the consistency of the estimators. Simulation studies and real data analysis show that the proposed estimation procedures work well.


heteroscedasticity, hierarchical models, semiparametric inference, Laplace’s approximation

Published 31 January 2017