Replication variance estimation in unequal probability sampling without replacement: One-stage and two-stage

2013 ◽  
Vol 41 (4) ◽  
pp. 696-716 ◽  
Author(s):  
C. Devon Lin ◽  
Wilson W. Lu ◽  
Keith Rust ◽  
Randy R. Sitter
Keyword(s):  
Variance Estimation ◽  
Two Stage ◽  
Sampling Without Replacement ◽  
Probability Sampling ◽  
Unequal Probability Sampling ◽  
One Stage ◽  
Unequal Probability

Evaluation of sampling alternatives to quantify tree leaf area

2003 ◽  
Vol 33 (1) ◽  
pp. 82-95 ◽  
Author(s):  
H Temesgen
Keyword(s):  
Leaf Area ◽  
Poor Performance ◽  
Tree Crown ◽  
Two Stage ◽  
Zero Bias ◽  
Probability Sampling ◽  
First Order ◽  
Unequal Probability Sampling ◽  
Unequal Probability ◽  
Tree Leaf

High within- and among-tree crown variation have contributed to the difficulty of tree-crown sampling and single-tree leaf area (area available for photosynthesis) estimation. Using reconstructed trees, simulations were used to compare five sampling designs for bias, mean square error (MSE), and distribution of the estimates. All sampling designs showed nearly zero bias. For most sample trees, stratified random sampling resulted in the lowest MSE values, followed by ellipsoidal, two-stage systematic, simple random, and then by two-stage unequal probability sampling. The poor performance of two-stage unequal probability sampling can be ascribed to the unequal probability of inclusion of first-order branches and twigs.

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