The estimators of V (ṫHT) in (6.22) and (6.23) require knowledge of the joint inclusion probabilities Ïik.
Question:
a. Does the set of ËÏiks satisfy condition (6.18)? Can they be joint inclusion probabilities?
b. What is ËÏik if an SRS is taken? Show that if N is large, ËÏik is close to Ïik .
c. Show that if ËÏik is substituted for Ïik in (6.21), the expression for the variance can be written as
Where ei = ti /Ïi A and
Write (6.21) as
d. We can estimate á¹¼Haj(ËtHT) by
Where
That if an SRS of size n is taken, then ṼHaj(ṫHT) = N2(1 n/N)s2 t /n.
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