cluster Two-stage sampling
Point estimator for mean per SSU
October 19, 2009
Population
Total # of PSUs = N .
# SSUs in ith PSU = Mi , i = 1, . . . , N .
N
i=1 Mi
=: K , i.e., K = total number of SSUs in population.
Sample
Take SRS(N ,n) of PSUs; then from ith sample PSU, take SRS(Mi ,mi ).
Estimand: mean population = K = mean per SSU. Estimator:
1
xcl :=
K
PSUs sample
N
Mi xi ,
n
where xi is the sample mean in the ith sampled PSU.
Variance estimate:
1
where
n
N
1
12
2 sb + nN M 2
nM
s2 =
b
PSUs sample
PSUs sample
Mi2 1
mi
Mi
(Mi xi M xcl )2 /(n 1)
1
s2
i
,
mi