Sampling with control on joint inclusion probabilities and its applications to balanced structures
LE3 .A278 2009
Master of Science
Mathematics and Statistics
Mathematics & Statistics
One of the evaluation criteria about the sampling schemes is whether the drawn sam-ples can be used to make precise inferences. Not only must the first order inclusion probabilities be met, but also the joint inclusion probabilities need to lead to a non-negative variance estimator. This thesis proposes a sampling scheme by controlling joint inclusion probabilities to support precise inferences. The effectiveness of the proposed approach is studied by comparing with an approach without control on joint inclusion probabilities. Then we extend this idea to construct balanced struc-tures. Through sampling, we study the construction of a Hadamard matrix with the help of controlling joint inclusion probabilities. As a result, an example of constructed Hadamard matrix is presented and the quality analysis for different orders of matrices is studied.
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