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European Association of Methodology

Department of methodology and evaluation research

Jena University


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Contributions: Abstract

Estimation of income with small sample sizes

Danute Krapavickaite
Institute of Mathematics and Informatics
Lithuania

The household budget survey (HBS) is one of the most important sample surveys in official statistics of every country. It estimates income in cash and kind and expenditure per capita of the population of the country and in various parts of the population.

The Lithuanian HBS uses a stratified two stage sampling design. Income per capita is estimated as the ratio of two totals. Both sample size and the accuracy of the estimates in the rural areas are low. Small area estimation methods using auxiliary information from the neighboring areas are applied in the paper in order to improve the accuracy of the estimates of the income per capita in the rural area of Lithuania.

Two kinds of small area estimators - the James-Stein estimator and the empirical best linear unbiased predictor (EBLUP) - are used with data of the Lithuanian HBS. The direct estimates, based on the sample design, and currently used calibrated estimates are also presented for comparison. Calibration of design weights is used to adjust the sample to the demographic data and to nonresponse (Deville et al.). Demographical data and agricultural production data are used to build an income model. The averages over small areas of the estimated mean square errors ([`(MSE)]) of estimates of income are used for comparison.

The James-Stein estimator performs better than the direct one. The MSE of the composite estimator EBLUP performs equally along the areas, improving a very low accuracy of the direct estimator in some areas, however, without any improvement in the average accuracy. This can be explained by the low correlation between the direct estimates in the areas and auxiliary variables. So, better auxiliary information has to be found. The currently used calibrated estimator has the smallest [`(MSE)].

References

J. Deville, C.-E. Särndal, and O. Sautory (1993).Generalized raking procedures in survey sampling.JASA, 88, 1013-1020.

R.E. Fay, and R.A. Herriot (1998). Estimates of income forsmall places: an application of James-Stein procedures to censusdata. JASA, 74, 269-277.

M. Ghosh, and J.N.K. Rao (1994). Small area estimation: anappraisal. Statistical Science, 9(1), 55-93.

D. Krapavickaite (2003) . An example of small area estimation infinite population sampling. Lietuvos matematikos rinkinys,43, (to appear).