Question

Consider a situation that a population of size M has been partitioned into to N primary units of sizes Mi 's. In the first stage, an unequal probability sample of n proportional to size (pi=Mi/M) is taken from primary units. In the second stage, an unequal probability sample of size mi is selected from unit i and the variable of study, yij, and auxiliary variable xij observed. The inclusion probability of unit j in primary unit i is π j|i (j conditional i). Derive, an estimator of, μy, population mean, and its variance estimator when Ratio estimator used in the second stage.

Answer 1

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