Danny Pfeffermann , Dano Ben-Hur , Olivia Blum
ARTICLE

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ABSTRACT

Like in many countries, Israel has a fairly accurate population register at the national level, consisting of about 9 million persons (not including Israelis living abroad). However, the register is much less accurate for small geographical (statistical) areas, with an average area enumeration error of about 13%. The main reason for the inaccuracy at the area level is that people moving in or out of an area are often late in reporting their change of address, and in some cases, not reporting at all. In order to correct the errors at the area level in our next census, we investigate the use of the following three-step procedure:
A- Draw a sample from an enhanced register to obtain initial direct sample estimates for the number of persons residing in each area on “census day”,
B- Fit the Fay-Herriot model to the direct estimates in an attempt to improve their accuracy,
C- Compute a final census estimate for each statistical area as a linear combination of the estimate obtained in Step B and the register figure.
We also consider a procedure to deal with not missing at random (NMAR) nonresponse in Step A. The proposed procedures are illustrated using data from the 2008 Census in Israel.

KEYWORDS

direct estimator, Fay-Herriot model, Missing Information Principle, NMAR nonresponse, Root MSE estimation

REFERENCES

BLUM, O., (2018). From physical area to virtual lists: Toward an administrative census in Israel. UNECE group of experts on population and housing censuses. Geneva.

FAY, R. E., HERRIOT, R. A., (1979). Estimation of income from small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association, 74, pp. 269–277.

ORCHARD, T., WOODBURY, M. A., (1972). A missing information principle: theory and application. Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, 1, pp. 697–715.

PFEFFERMANN, D., BEN-HUR, D., (2018). Estimation of Randomization Mean Square Error in Small Area Estimation. International Statistical Review, 0, 0, pp. 1–19, DOI:10.1111/insr.12289.

SVERCHKOV, M., PFEFFERMANN, D., (2018), "Small area estimation under informative sampling and not missing at random non-response". Journal of the Royal Statistical Society, Series A, 181, pp. 981–1008.

YBARRA, L. M. R., LOHR, S. L., (2008), Small area estimation when auxiliary is measured with error, Biometrika, 95, pp. 919–931.

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