A Sampling Procedure for Historical Data

Summary

For historical data,a sampling plan is designed meeting the following conditions:

• (i) Clusters (in the sense of sampling theory) are not pregiven but have to be determined yet (clustering in the sense of automatic classification).

• (ii) Sampling should be optimal in the sense of minimum variance estimators, taking into account restrictions on costs, time, and manpower.

• (iii) Independence of scaling and projections has to be ensured.

A single-stage cluster sampling plan with unequal sizes of clusters is developed, using non-linear optimization techniques and a Cayley-Klein projective metric.