PALESTINIAN SOCIETY - Fafo

ff the variable is defined according to households, the "x-aggregate"
of the household is of course the observation itself:
� (s, k, c, h, d) = XT (s, k, c, h, d)
By aggregating step by step through the various sampling stages,
we obtain estimates for the respective sampling unit sums by summation
of weighted observations, the weights being the inverse of the
incIusion probabilities at each stage (Horvitz-Thompson estimator):
. Estimated x-total for housing unit (s,k,c,h):
x;. (s, k, c, h) = L xT (s; k, c, h, d)
d P 4 (s, k, c, h, d)
where the 4th stage inclusion probability is
1
P4 (s, k, c, h, d) = D (s, k, c, h)
for alfhouseholds, d, of the housing unit, d= 1 , ... , D(s,k,c,h). Estimate
of ceIl(s,k,c) x-total:
'" � X"T (s, k, c, h)
xT (s, k, c) = � p (5 k c h)
h 3 " I
where the 3rd stage inclusion probability is
P ( k h) d (5, k, c)
3 S, ,c, = H (s, k, c)
for all housing units of the ceII, h=I, ... ,H(s,k,c).
Estimated PSU (s,k) x-total:
� xT (s, k, c)
'"
xT (s, k) =: � . . P2 (5, k, c)
where the 2nd stage inclusion probability is
b (s, k)
P 2 (5, k, c) = B (s, k)
for all ceIIs of tile PSU, c=I, ... ,B(s,k).
For the s-th stratum the x-total estimate is:
� �T (s, k)
'"
� (s) = � Pl (s, k)
where the 1st stage incIusion probabilities have been defmed in
previous sections, and k=l, ... ,K(s).
Finally we have the estimate for the aggregate total for all strata:
(5.1) x,. = L xT (5)
,
. S .
This estimator is unbiased.
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