Dees, Matthias 
  
In simple random sampling, the mean is estimated by 
$= vIn (D 
k=l 
and the variance of the estimator is estimated by 
e ; 
V ie Mie he Yom Q) 
with y, - the value of the attribute y on element k, that is one of the elements out of the sample k=I..n of size n 
(Cochran, 1976). In simple random sampling the ratio is estimated approximately unbiased by 
  
R,, = P. = Yor 3) 
I z 
„STS 
rs 
where : is the symbol for sums and the variance of the estimator is estimated by 
  
VR.) -s * Rs? -2R,s,.] (4) 
with 
-N ny iA In) n (Q, -Y y, /mG, - Y 3, Im) 
2 -— k=1 . 2 = = k=l k=1 
SEA n-1 PST g^ n-1 (5. 2 y--] 
(Särndal et al, 1992, Dees, 1996) with z, -the value of the attribute z on element k and where 2. , 1$ defined according 
to e 
In stratified sampling with simple random sampling of n, elements (k—1..ny) within A strata (h— 1.. H) the mean is 
estimated as 
n, 
a H 
mW WI (5) 
h=1 =1 5g, 
with the strata specific weights W - [Area of Strata h] / [total area]. 
The variance of the estimated mean is estimated by 
x INS Ya) 
Rn H 
(E M AE on (6) 
n, 
(Cochran, 1976, Sárndal et al., 1992). 
In stratified sampling with simple random sampling within the strata, the ratio is estimated approximately unbiased as 
> 
^ 
= y,strat = Y errat (7) 
Z 
> 
~ 
strat 
et. 
z,strat strat 
The variance of the estimated ratio is estimated by 
  
358 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.