MC Simulation of SEBLUP with Spatial Linear Mixed Model for SAE

Article Preview

Abstract:

For small area estimation (SAE) Spatial Empirical Best Linear Unbiased Prediction, SEBLUP, is involved in linear mixed model with spatial correlation while Empirical Best Linear Unbiased Prediction, EBLUP, often with mutual independence. In this paper, we discussed maximum likelihood estimation (MLE) and compared the efficiency. Simulation shows that SEBLUP with spatial correlation data of spatial small area is more effective than EBLUP.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

618-622

Citation:

Online since:

October 2014

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] I. Molina, J.N.K. Rao: Small area estimation of poverty indicators. Canadian Journal of Statistics, Vol 38(3) (2010), p.369–385.

DOI: 10.1002/cjs.10051

Google Scholar

[2] W.S. CHAN: Maximum Likelihood Estimation Mixed Models Using Monte Carlo to Small Area Estimation in Generalized Linear Methods: Application of Breast Cancer Mortality. Applied Probability and Statistics (in Chinese), Vol 22(1) (2006), pp. l-22.

Google Scholar

[3] L.P. Liu. S.Q. Pan and X.M. Ren: Small Area Estimation of Disability Base on Hierarchical Bayesian Statistics. Statistical Research (in Chinese), Vol. 27(3) (2010), pp.83-88.

Google Scholar

[4] J.N.K. Rao: Small Area Estimation Hoboken[ M]. New York: Wiley, (2003).

Google Scholar

[5] M. Pratesi and N. Salvati: Small area estimation: the EBLUP estimator based on spatially correlated random area effects. Stat. Meth. & Appl., Vol. 17(1) (2008), p.113–141.

DOI: 10.1007/s10260-007-0061-9

Google Scholar

[6] H. Li andP. Lahiri: An adjusted maximum likelihood method for solving small area estimation problems. Journal of Multivariate Analysis, Vol. 101(4) (2010), pp.882-892.

DOI: 10.1016/j.jmva.2009.10.009

Google Scholar

[7] R. E. Fay III and R. A. Herriot: Estimates of Income for Small Places. An Application of James-Stein Procedures to Census Data [J]. Journal of the American Statistical Association, Vol. 74(366a) (1979), pp.269-277.

DOI: 10.1080/01621459.1979.10482505

Google Scholar

[8] Y.T. Zhang: Spacial Statistics. Statistics Education(in Chinese), Vol. 10(1)(1996), pp.35-40.

Google Scholar

[9] D. Bates, M. Mächler and B. Bolker: Fitting linear mixed-effects models using lme4[J]. Journal of Statistical Software (forthcoming), (2012).

DOI: 10.18637/jss.v067.i01

Google Scholar

[10] T. A. Davis: Direct Methods for Sparse Linear System. Fundamentals of Algo. SIAM, (2006).

Google Scholar

[11] D. Bates: Mixed-effects modeling with R [EB/OL](2010). information on http: /lme4. r-forge. r- project. org/lMMwR/lrgprt. pdf.

Google Scholar

[12] D.A. Harville andD.R. Jeske: Mean squared error of estimation or prediction under a general linear model. Journal of the American Statistical Association, Vol. 87(419)(1992), p.724–731.

DOI: 10.1080/01621459.1992.10475274

Google Scholar

[13] D. L. Zimmerman and N. Cressie: Mean squared prediction error in the spatial linear model with estimated covariance parameters . Annals of the institute of statistical mathematics, Vol. 44(1)(1992), p.27–43.

DOI: 10.1007/bf00048668

Google Scholar

[14] J.F. Yang, M. Zhao and W.S. Hu: Web Software Reliability Analysis Based on NHPP Class Model(in Chinese). Computer Engineering Vol. 38(14)(2012). p.26—28.

Google Scholar

[15] G. Sofronov: Spatial Approaches in Small Area Estimation. (2009) Information on http: / www. uow. edu. au/content/groups/public/@web/@inf/@math/ documents/web/uow054844. pdf.

Google Scholar