|Table of Contents|

[1] Xu Weijuan, Lin Jinguan,. Diagnostics in generalized nonlinear modelsbased on maximum Lqq-likelihood estimation [J]. Journal of Southeast University (English Edition), 2013, 29 (1): 106-110. [doi:10.3969/j.issn.1003-7985.2013.01.022]

Diagnostics in generalized nonlinear modelsbased on maximum Lqq-likelihood estimation()

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

2013 1
Research Field:
Mathematics, Physics, Mechanics
Publishing date:


Diagnostics in generalized nonlinear modelsbased on maximum Lqq-likelihood estimation
Xu Weijuan Lin Jinguan
Department of Mathematics, Southeast University, Nanjing 211189, China
maximum Lqq-likelihood estimation generalized nonlinear regression model case-deletion model generalized Cook distance likelihood distance difference of deviance
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lqq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lqq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lqq-likelihood method than those through the maximum likelihood estimation method.


[1] Cook R D, Weisberg S. Residual and influence in regression [M]. London: Chapman and Hall, 1982.
[2] Chatterjee S, Hadi A S. Influential observations, high leverage points and outliers in linear regression(with discussion)[J]. Statistical Science, 1986, 1(3): 379-416.
[3] McCullagh P, Nelder J A. Generalized linear models [M]. London: Chapman and Hall, 1989.
[4] Davison A C, Tsai C L. Regression model diagnostics [J]. International Statistical Review, 1992, 60(3): 337-355.
[5] Gay D M, Welsch R E. Maximum likelihood and quasi-likelihood for nonlinear exponential family regression models [J]. Journal of the American Statistical Association, 1988, 83(404): 990-998.
[6] Wei B C and Shi J Q. On statistical models in regression diagnostics [J]. Ann Inst Statist Math, 1994, 46(2):267-278.
[7] Wei B C. Exponential family nonlinear models [M]. Singapore: Springer, 1998.
[8] Ferrari D, Yang Y. Estimation of tail probability via the maximum Lq-likelihood method [R]. Minneapolis, MN, USA: School of Statistics, University of Minnesota, 2007.
[9] Kullback S. Information theory and statistics [M]. Wiley: New York, 1959.
[10] Shannon C E. A mathematical theory of communication [J]. Bell System Technical Journal, 1948, 27:379-423.
[11] Havrda J, Charvát F. Quantification method of classification processes: concept of structural entropy [J]. Kibernetika, 1967, 3: 30-35.
[12] Whitmore D A. Inverse Gaussian ratio estimation [J]. Journal of the Royal Statistical Society, Series C(Applied Statistics), 1986, 35(1):8-15.
[13] Wei B C, Lin J G, Xie F C. Statistical diagnosis [M].Beijing: Higher Education Press, 2009.(in Chinese).


Biographies: Xu Weijuan(1977—), female, graduate; Lin Jinguan(corresponding author), male, doctor, professor, jglin@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11171065), the Natural Science Foundation of Jiangsu Province(No.BK2011058).
Citation: Xu Weijuan, Lin Jinguan.Diagnostics in generalized nonlinear models based on maximum Lqq-likelihood estimation[J].Journal of Southeast University(English Edition), 2013, 29(1):106-110.[doi:10.3969/j.issn.1003-7985.2013.01.022]
Last Update: 2013-03-20