Page 147 - Contributed Paper Session (CPS) - Volume 6

CPS1851 Hee Young Chung et al.
substrata. That is, dividing the stratum by auxiliary variable into substrata gives
1
the value of the weight . Also using ( | , ) = ( | , ) and

( | , ) ≈ from Pfeffermann and Sverchkov (2003) and obtained by

substrata, we can construct the following model.

1
log ( ) = + + (5)

0
1

Finally, can be estimated using (5).
1

3. Estimation of bias on a linear non-response rate model
a. Sample distribution and bias estimation
In this study we consider the error of the super population model follows
the normal distribution and the population distribution is given by (2). Also,
we consider the linear response rate model as follows.

( | , ) = + (6)

0
1

Then simply we have the following result.

( | ) = ( ( | , )) = ( + | )

1
0

(7)
= + ( | )
0
1

Now, using the equations (6) and (7), we get the following result.

( | , ) +
= 0 1 (8)
( | ) + ( | )

0

1

Substituting equation (8) into equation (1), the following result is obtained.

+
0
1
( | ) = + ( | ) ( | )

1
0

0 1
= ( | ) + ( | )
+ ( | ) + ( | )

1

1
0
0

∗
Now let ( | ) be a distribution of ( | ). Then it becomes simply the

following form.

0
( | ) = + ( | ) ( | )

0 1 (9)

1
∗
+ ( | )
+ ( | )

0

1
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