The Rao-Hartley-Cochran (1962) method for selecting psus with unequal probabilities. To take a sample of size n, divide the population into n random groups of psus, U₁, U₂, . . . ,U_n. Then select one psu from each group with probability proportional to size. Let Nk be the number of psus in group k. If psu i is in group k, it is selected with probability xki = M_i / Ʃ_{j∈Uk Mj} ; the estimator is

Show that ṫ_RHC is unbiased for t, and find its variance. Use two sets of indicator variables. Let I_ki = 1 if psu i is in group k and 0 otherwise, and let Z_i = 1 if psu i is selected to be in the sample.

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RHC Xki に!