Small Area Estimation and Spaial Prediction

Document Type : Original Paper

Authors

1 Professor in Statistics at Tarbiat Modares University

2 Department of Statistics, Tarbiat Modares University

Abstract

Direct estimators of parameters are not precise because of little surveys unit in small areas. Regarding the wide spread increase of demand for providing valid and accurate statistics for small areas, attempts have been made to present proper solutions for the problems. Small area estimation approaches provide the direct estimators with borrowing strength to increase their precision based on a model, especially about those estimators that are based on the linear mixed model including random area effects and using various auxiliary sources. Data associated with spatially contiguous small areas may be modeled via covariates, with error terms that are spatially dependent according to neighbor areas. In this paper we investigate small area estimation based on linear models with spatially correlated small area effects where the neighborhood structure is described by a contiguity matrix. Such models allow efficient use of spatial auxiliary information in small area estimation. Then estimation for small areas will be achieved for the amount of agronomy production in Fars province, according to the two common EBLUP and MBDE methods and two usual (non spatial) and spatial approaches based on the unit level model. Then the accuracy of them have been compared.

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Main Subjects


[1] Rao‎, ‎J‎. N‎. K‎. ‎(2003)‎, Small Area Estimation‎, ‎John Wile‎, ‎New York‎.
[2] Chambers‎, ‎R‎.‎ L‎. ‎and Chandra‎, ‎H‎. ‎(2006)‎, Improved Direct Estimators for Small Area, ‎Centre for Survey Statistics and Methodology‎, University of Wollongong, Working Paper 03-08, 2008, 26p.
[3] Fuller‎, ‎W‎.‎A‎. ‎and Harter‎, ‎R‎.‎M‎. ‎(1987)‎, The Multivariate Components of Variance Model for Small Area Estimation‎, ‎In Platek‎, ‎R.‎, ‎Rao‎, ‎J‎. ‎N‎.‎ K.‎, ‎Sarndal‎, ‎C‎. ‎E‎. ‎and Singh‎, ‎M‎.‎P‎. ‎(Eds.)‎, ‎Small Area Statistics‎, ‎John Wiley and Sons‎, ‎New York‎.
‎[4] Royall‎, ‎R‎.‎M‎. ‎and Cumberland‎, ‎W‎.‎G‎. ‎(1978)‎, ‎Variance Estimation in Finite Population‎‎Sampling‎, Journal of the American Statistical Association‎, 73‎, ‎351-358‎.
[5] Cressie‎, ‎N‎. ‎(1991)‎, ‎Small Area Prediction of Undercount Using the General Linear Model‎, Proceeding of Statistics Canada Symposium, 90‎, ‎93-105‎.
[6] Chandra‎, ‎H.‎, ‎Salvati‎, ‎N‎. ‎and Chambers‎, ‎R‎. ‎(2007)‎, Small Area Estimation for Spatially Correlated Populations-A Comparison of Direct and Indirect Model Based Methods‎, Statistics in Transition‎, 8, ‎331-350‎.
[7] Anselin‎, ‎L‎. ‎(1992)‎, Method and Models‎, ‎Kluwer Academic Publishers‎, ‎Boston‎.
[8] Banerjee‎, ‎S.‎, ‎Carlin‎, ‎B‎. ‎and Gelfand‎, ‎A‎. ‎(2004)‎, Hierarchical Modelling and Analysisfor Spatial Data‎, ‎Chapman and Hall‎, ‎New York‎.
[9] Petrucci‎, ‎A‎. ‎and Salvati‎, ‎N‎. ‎(2006)‎, ‎Small Area Estimation for Spatial Correlation in Watershed Erosion Assessment‎, Journal of Agricultural, Biological and Environmental Statistics, 11‎, ‎169-182‎.
[10] Nelder‎, ‎J‎. ‎and Mead‎, ‎R‎. ‎(1965)‎, ‎A Simplex Method for Function Minimization‎, Computer Journal‎, 7‎, ‎308-313‎.
[11] Moran‎, ‎P‎. A‎. ‎P‎. ‎(1950)‎, ‎Notes on Continuous Stochastic Phenomena‎, Biometrika‎, 37‎, ‎17-23‎.
[12] باذل، ف. ‎(۱۳۹۱)‎، روش وزن‌دهی در برآورد کوچک ناحیه‌ای، پایان‌نامه کارشناسی ارشد، دانشگاه تربیت مدرس.