On Precision in Estimates of Change over Time where Samples are Positively Coordinated by Permanent Random Numbers

Abstract

Measures of period-to-period change are key statistics for many economy surveys. To improve the precision of these estimates of change, the majority of the business surveys at Statistics Sweden select stratified simple random samples (STSI) at different points in time, ensuring positive correlation between samples (overlapping samples) by using permanent random numbers (PRN). Statistics Sweden normally selects positively coordinated STSIs drawn from an updated Business Register (BR). In these samples, the industry strata are usually stratified further within industry into size strata. When the most recent sampling frame contains updated classification variables for all units, enterprises can change stratum between two sampling occasions. A drawback of the coordinated sample selection procedure is that the desired correlation between the two samples decreases if the proportion of enterprises that change strata is substantial. Consequently, the sample design must anticipate the potential effect of stratum changes between samples. This article presents a study that examines how the design of a repeated business survey affects the precision in estimates of change over time using the Turnover in the Service Sector survey conducted by Statistics Sweden as an example.

Keywords

Measures of change sample coordination survey design variance estimation

References

Berger, Y. 2004. “Variance Estimation for Measures of Change in Probability Sampling.” The Canadian Journal of Statistics 32: 451-467. DOI: https://dx-doi-org.web.bisu.edu.cn/10.2307/3316027.

Dalenius, T. and J.L. Hodges. 1959. “Minimum Variance Stratification.” Journal of the American Statistical Association 54: 88-101. DOI: https://dx-doi-org.web.bisu.edu.cn/10.2307/2282141.

Fishman, G.S. and L.R. Moore. 1982. “A Statistical Evaluation of Multiplicative Congruential Random Number Generators with Modulus 231-1.” Journal of the American Statistical Association 77: 29-136. DOI: https://dx-doi-org.web.bisu.edu.cn/10.1080/01621459.1982.10477775.

Garås, T. 1989. Estimators of Change in Dynamic Populations. Memo: Statistics Sweden. (In Swedish).

Hidiroglou, M., C.-E. Särndal, and D. Binder. 1995. “Weighting and Estimation in Business Surveys.” In Business Survey Methods, edited by B.G. Cox, D.A. Binder, B.N. Chinnappa, A. Christianson, M. Colledge, and P.S. Scott, 477-502. New York: John Wiley & Sons.

Laniel, N. 1988. “Variances for a Rotating Sample from a Changing Population.” In Proceedings of the Business and Economic Statistics Section: American Statistical Association. 246-250.

Lindblom, A. 2003. SAMU - The System for Coordination of Frame Populations and Samples from the Business Register at Statistics Sweden. Background Facts on Economic Statistics 2003:3, Statistics Sweden. Available at: http://www.scb.se/statistik/OV/AA9999/2003M00/X100ST0303.pdf (accessed September 1, 2014).

Neyman, J. 1934. “On the Two Different Aspects of the Representative Method: The Method Stratified Sampling and the Method of Purposive Selection.” Journal of Royal Statistical Society 97: 558-606. DOI: https://dx-doi-org.web.bisu.edu.cn/10.2307/2342192.

Nordberg, L. 2000. “On Variance Estimation for Measures of Change When Samples are Coordinated by the Use of Permanent Random Numbers.” Journal of Official Statistics 16: 363-378. Available at: http://www.jos.nu/Articles/abstract.asp?article¼164363 (accessed September 1, 2014).

10.

Ohlsson, E. 1992. SAMU - The System for Co-ordination of Samples from the Business Register at Statistics Sweden. R&D Report, Statistics Sweden, 1992:18.

11.

Ohlsson, E. 1995. “Coordination of Samples using Permanent Random Numbers.” In Business Survey Methods, edited by B. Cox, D. Binder, B. Chinnappa, A. Christianson, M. Colledge, and P. Kott, 153-169. New York: John Wiley.

12.

Särndal, C.-E., B. Swensson, and J. Wretman. 1992. Model Assisted Survey Sampling. New York: Springer-Verlag.

13.

Tam, S.M. 1984. “On Covariances from Overlapping Samples.” The American Statistician 38: 288-292. DOI: https://dx-doi-org.web.bisu.edu.cn/10.1080/00031305.1984.10483227.

14.

Wood, J. 2008. “On the Covariance Between Related Horvitz-Thompson Estimators.” Journal of Official Statistics 24: 53-78. Available at: http://www.jos.nu/Articles/abstract.asp?article¼241053 (accessed September 1, 2014).