Exploring the properties of the UEPSWOR sampling algorithms via simulations
LE3 .A278 2016
Master of Science
Mathematics and Statistics
Mathematics & Statistics
Unequal probability sampling without replacement (UEPSWOR) is an efficient sampling technique for certain survey sampling scenarios. Among available UEPSWOR designs, there are some methods that can compute the joint inclusion probability. However, computing the joint inclusion probability is still a complicated procedure. In 1952, Horvitz and Thompson proposed the well known Horvitz-Thompson (H-T) estimator of the population total, bYHT , as well as an unbiased variance estimator of bYHT. The Horvitz-Thompson variance estimator of bYHT, however, is not very stable as it sometimes produces negative values. In 1953, Sen, Yates and Grundy proposed another unbiased variance estimator of bYHT and made sure it would not produce negative values as long as the condition, fij 6 0, holds for all pairs of (i;j). Any sampling scheme that draws samples under unequal probability sampling without replacement with fixed sample size, must respect the pre-determined inclusion probabilities. Recently, new sampling designs such as maximum entropy design and Lu's algorithm were proposed. This thesis discusses Lu's algorithm in detail and uses a simulation study to suggest that Lu's algorithm has more exibility in accommodating different sampling scenarios while providing equally satisfactory results in variance estimation.
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