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A prediction approach to representative sampling

The birth of representative method. Kruskal and Mosteller (1979a,b,c): origins and development of the concept representative samplingN. Ki

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A prediction approach to representative sampling

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    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. Kićr’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 Kićr 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

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