[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7465/jkdi.2015.26.2.465

The local influence of LIU type estimator in linear mixed model

Zhang, Lili (Department of Statistics, Chonnam National University)
Baek, Jangsun (Department of Statistics, Chonnam National University)

Publication Information

Journal of the Korean Data and Information Science Society / v.26, no.2, 2015 , pp. 465-474 More about this Journal

Abstract

In this paper, we study the local influence analysis of LIU type estimator in the linear mixed models. Using the method proposed by Shi (1997), the local influence of LIU type estimator in three disturbance models are investigated respectively. Furthermore, we give the generalized Cook's distance to assess the influence, and illustrate the efficiency of the proposed method by example.

Keywords

Generalized Cook's distance; linear mixed model; LIU type estimator; local influence;

Citations & Related Records

Reference

1	Beckman, R. J., Nachtsheim, C. J. and Cook, R. D. (1987). Diagnostics for mixed-Model of variance. Journal of Technometrics, 29, 413-426.
2	Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of colinearity, John Wiley, New York.
3	Chatterjee, S. and Hadi, A. S. (1988). Sensitivity analysis in linear regression, John Wiley, New York.
4	Cook, R. D. (1986). Access of local influence. Journal of the royal statistical society, 48, 133-169.
5	Cook, R. D. and Weisberg, S. (1982). Residuals and influence in regression, John Wiley, New York.
6	Lawrance, A. J. (1988). Regression transformation diagnostics using local influence. J. Am. Statist. Assoc., 83, 1067-1072. DOI ScienceOn
7	Li, Y. L. and Yang, H. (2012). A new Liu-type estimator in linear regression model. Springer-Verlag, 53, 427-437.
8	Liu, K. J. (1993). A new class of biased estimate in linear regression. Journal of Commun. Statist. Theo. and Meth., 22, 393-402. DOI
9	Liu, K. J. (2004). More on Liu-type in estimator in linear regression. Communications in Statistics-Theory and Methods, 33, 223-2733.
10	Liu, X. Q. (2011). Improved Liu estimator in a linear regression model. Journal of Statistical Planning and Inference, 141, 189-196. DOI ScienceOn
11	Myers, R. H. (1986). Classical and modern regression with applications, Duxbury Press, Boston.
12	Ronald, C. and Larry, M. P. (1992). Case deletion diagnostics for mixed models. Technometrics, 34, 38-45. DOI ScienceOn
13	Rousseeuw, P. J. and Leroy, A. M. (1987). Robust regression and outlier detection, John Wiley and Sons, New York.
14	Shi, L. (1997). Local influence in principal components analysis. Biometrika, 84, 175-186. DOI ScienceOn
15	Shi, L. (1999). Local influence in ridge regression. Computational Statistics and Data Analysis, 31, 341-353. DOI ScienceOn
16	Shi, L. and Chen, G. M. (2008). Case deletion diagnostics in multilevel models. Journal of multivariate Analysis, 99, 1860-1877. DOI ScienceOn
17	Shi, L., Xiang, L. M. and Wang, X. R. (1996). Local influence of eect parameter in linear mixed model. Acta Mathematica Scientia, 16, 316-323.
18	Thomas, W. and Cook, R. D. (1990). Assessing influence on predictions from generalized linear models. Technometrics, 32, 59-65. DOI ScienceOn
19	Zhang, L. L. and Zhang, S. L. (2010). Local influence analysis of Liu estimate in linear model. Journal of information and computational science 7, 13, 2731-2737.