= Double Sampling =

'''Double Sampling''' was written by Michael Hidiroglou in 2001. It was published in ''Survey Methodology'' (vol. 27, no. 2).

The theory of double sampling, or two-phase sampling, is introduced. The core concept is that there are two samples, one nested in the other. Notation used is:
 * population ''U = {1, ..., N}''
 * first sample ''s,,1,,(s,,1,, ⊆ U)''
 * first sample inclusion probability for unit ''k'': ''π,,1k,, = P(k ∈ s,,1,,)''
 * first sample weight ''w,,1,, = 1/π,,1k,,''
 * second sample ''s,,2,,(s,,2,, ⊆ s,,1,, ⊆ U)''
 * second sample inclusion probability for unit ''k'', given the first sample: {{attachment:s2.svg}}
 * second sample weight ''w,,2,, = 1/π,,2k,,''
 * overall sample weight ''w*,,k,, = w,,1,, w,,2,,''
 
The author then derives estimators that can be used in both nested and non-nested cases.

Unfortunately this math is a bit beyond me right now.



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