Evaluation of variance approximations and estimators in maximum entropy sampling with unequal probability and fixed sample size

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A Direct Bootstrap Method for Complex Sampling Designs From a Finite Population (2011, background): “When the entropy of the sampling design is large, biased estimators given in (8), (9), and (10) have a smaller mean square error than estimators (2) and (4) (see Matei and Tillé 2005).”
Pareto Sampling versus Sampford and Conditional Poisson Sampling (2006, result): “Aires (1999) and Matei & Tillé (2005) argue for use of the simpler iterative formula: p(m+1)i =p(m)i + i − (m)i that at least empirically seems to work well.”