Trade-off between efficiency and variance estimation of spatially balanced augmented samples

Aronow PM, Samii C (2013) Conservative variance estimation for sampling designs with zero pairwise inclusion probabilities. Surv Methodol 39(1):231–241

Benedetti R, Piersimoni F, Postiglione P (2015) Sampling balanced sampling: a review and a reappraisal. Int Stat Rev 85(439–454):15

Benedetti R, Piersimoni F (2017) A spatially balanced design with probability function proportional to within sample distance. Biom J 59:1067–1084

Dickson MM, Tillé Y (2016) Ordered spatially balanced sampling by means of the traveling salesman problem. Comput Stat 31:1359–1372

Grafström A (2011) Spatially correlated Poisson sampling. J Stat Plann Inference 142:36–41

Grafström A, Lundström NLP, Schelin L (2012) Spatially balanced sampling through the pivotal method. Biometrics 68:514–520

Grafström A, Lundström NLP (2013) Why well spread probability samples are balanced. Open J Stat 3:36–41

Grafström A, Tillè Y (2013) Doubly balanced sampling with spreading and restitution of auxiliary totals. Environmetrics 14:120–131

Grafström A, Matei A (2018) Spatially balanced sampling of continuous populations. Scand J Stat 45:792–805

Grafström A, Schelin L (2014) How to select representative samples. Scand J Stat 41:277–290

Halton JH (1960) On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer Math 2:84–90

Kermorvant C, D’Amico F, Bru N, Caill-Milly N, Robertson B (2019) Spatially balanced sampling designs for environmental surveys. Environ Monitor Assess 191:524

King AJ (1945) The master sample of agriculture. J Am Stat Assoc 40:38–45

Larsen DP, Olsen AR Jr, Stevens DL (2008) Using a master sample to integrate stream monitoring programs. J Agric Biol Environ Stat 13:243–254

Price CJ, Price CP (2012) Recycling primes in the Halton sequence: an optimization perspective. Adv Model Optim 14:17–29

Robertson BL, Brown JA, McDonald T, Jaksons P (2013) BAS: balanced acceptance sampling of natural resources. Biometrics 3:776–784

Robertson BL, McDonald T, Price CJ, Brown JA (2017) A modication of balanced acceptance sampling. Stat Probab Lett 129:107–112

Robertson BL, McDonald T, Price CJ, Brown JA (2018) Halton iterative partitioning: spatially balanced sampling via partitioning. Environ Ecol Stat 25:305–323

Robertson BL, Reale M, Price CJ, Brown JA (2021) Quasi-random ranked set sampling. Stat Probab Lett. https://doi.org/10.1016/j.spl.2020.109029

Robertson BL, Ozturk O, Kravchuk O, Brown JA (2022) Spatially balanced sampling with local ranking. J Agric Biol Environ Stat 27:622–639. https://doi.org/10.1007/s13253-022-00501-6

Sen AR (1953) On the estimate of the variance in sampling with varying probabilities. J Indian Soc Agric Stat 5:119–127

Stevens DL Jr, Olsen AR (1999) Spatially restricted surveys over time for aquatic resources. J Agric Biol Environ Stat 4:415–428

Stevens DL Jr, Olsen AR (2004) Spatially balanced sampling of natural resources. J Am Stat Assoc 99(465):262–278

Stevens DL Jr, Olsen AR (2003) Variance estimation for spatially balanced samples of environmental resources. Environmetrics 14:593–610

Theobald DM, Stevens DL Jr, White DE, Urquhart NS, Olsen AR, Norman JB (2007) Using GIS to generate spatially balanced random survey designs for natural resource applications. Environ Manag 40:134–146

van Dam-Bates P, Gansell O, Robertson BL (2018) Using balanced acceptance sampling as a master sample for environmental surveys. Methods Ecol Evol 9:1718–1726

Wang X, Hickernell FJ (2000) Randomized Halton sequences. Math Comput Model 32:887–899

Yates F, Grundy PM (1953) Selection without replacement from within strata with probability proportional to size. J R Stat Soc Ser B 15:253–261

Yates F (1981) Sampling methods for censuses and surveys, 4th edn. Griffin, London