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Mathematical Problems in Engineering
Volume 2013, Article ID 547874, 13 pages
Research Article

Robust SiZer Approach for Varying Coefficient Models

1School of Mathematics and System Science, Xinjiang University, Urumqi 830000, China
2Department of Statistics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
3School of Applied Mathematics, Xinjiang University of Finance and Economics, Urumqi 830000, China

Received 12 January 2013; Accepted 15 April 2013

Academic Editor: Joao B. R. Do Val

Copyright © 2013 Hui-Guo Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Varying coefficient models have widely been applied to many practical fields for exploring dynamic patterns of the regression relationships. In this study, we propose a robust scenario of SiZer (significant zero crossing of derivatives) inference approach based on the local least absolute deviation fitting procedure and the bootstrap confidence interval to uncover the statistically significant features of the coefficient functions in a varying coefficient model under different smoothing scales. The simulation study shows that the proposed SiZer approach is quite robust to outliers and performs well in finding the significant features of the coefficient functions. Furthermore, a real environmental data set is analyzed to demonstrate the application of the proposed approach.