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Table 2 Data sources and sampling designs for REDD monitoring

From: Implications of sampling design and sample size for national carbon accounting systems

Data sources Sampling design Estimation procedures for means and variances of the mean (from [15])
Field plots Simple random sampling y ¯ = i = 1 n y i n ; v( y ¯ )= i = 1 n ( y i y ¯ ) 2 n ( n 1 )
  Systematic sampling  
Field plots & full coverage remote sensing imagery Stratified sampling
Example: field plots and Spot satellite imagery
y ¯ st = h = 1 L A h A i = 1 n h y hi n h
v ( y ¯ st ) = h = 1 L ( A h A ) 2 s h 2 n h ;
  Regression estimators
Example: field plots and TerraSarX (radar)
y ¯ lr = y ¯ + b( X ¯ x ¯ )
v ( y ¯ lr ) i = 1 n [ ( y i y ¯ ) b ( x i x ¯ ) ] 2 n(n 2)
Field plots & partial coverage remote sensing imagery 2-phase sampling for stratification (double sampling for stratification)
Example: field plots & aerial photography
y ̄ ds = h = 1 L n h n’ y ̄ h = h = 1 L w h y ̄ h
v ( y ¯ ds ) = N - 1 N h = 1 L ( n h - 1 n  - 1 - n L - 1 N - 1 ) W h - s h 2 n + N - n N(n - 1 ) h = 1 L W h y ¯ h - y ¯ ds
where
s h 2 = 1 n h h = 1 L ( y h i - y ¯ h ) 2
  2-phase sampling with regression estimators
Example: field plots & LiDAR
y ¯ lr = y ¯ + b( x ¯ ' x ¯ )
v ( y ¯ l r ) = s y . x 2 [ 1 n + ( x ¯ ' x ¯ ) 2 ( x ¯ ' x ¯ ) 2 ] + s y 2 s y . x 2 n ' s y 2 N
with s y . x 2 = 1 n 2 [ i = 1 n ( y i y ¯ ) 2 b 2 i = 1 n ( x i x ¯ ) 2 ]
  1. Where:
  2. yi = observation on field plot i; xi = observation in phase-1 sampling unit i; n = sample size, nh = sample size in stratum h; b = regression coefficient; N = population size; wh = weight of stratum h = Ah/A;
  3. A = inventory area; Ah = area in stratum h, h = 1, ..., L; sh2 = variance of y in stratum h;
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