A prediction approach to representative sampling

1. A prediction approach to representative sampling Ib Thomsen & Li-Chun Zhang Statistics Norway E-mail: lcz@ssb.no

2. The birth of representative method Kruskal and Mosteller (1979a,b,c): origins and development of the concept representative sampling N. Ki�r�s representative method (ISI meeting, 1895, Bern) A three-stage design, with 1890 census as frame: 1st: 128 counties and 23 towns throughout the country 2nd: cohorts of males of age 17, 22, 27, 32, etc. 3rd: persons with surname initial A, B, C, L, M, N Comparison of sample marginal averages with census averages ISI committee in 1924 & report at the following meeting: �I think I may venture to say that nowadays there is hardly one statistician, who in principle will contest the legitimacy of the representative method�. (Jensen) Bowley (1926) member of the committee.

3. Rise and fall of the representative method:Balance vs. randomization Ki�r did not take a probabilistic point of view. Representative sample surveys instead of representative sampling Idea of variability of population over time (quote) Miniature population ? multivariate simple balance Design-based approach: Neyman (1934): representative sampling = randomization (quote) Subsequent development: Hansen & co., Deming, Kish, Cochran, Mahalanobis, etc. Godambe (1955): no minimum variance linear estimator Representative sampling vs. efficient estimation Prediction approach: Royall (1970): purposive sample Royall and Eberhardt (1975): Simple balance for bias protection (quote) Representative sample vs. efficiency

4. A definition of representative sampling from a prediction point of view Prediction of each individual in the population Representative sampling connected to individual mean squared error of prediction (IMSEP), i.e. Conditional IMSEP: zero inside the sample, positive outside Use randomization design to control unconditional IMSEP, i.e. expected amount of information about each population unit. Control of individual prediction as a design criterion, i.e.

5. An example under ratio model