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A new resampling method for sampling designs without replacement: the doubled half bootstrap

Published: 01 October 2014 Publication History

Abstract

A new and very fast method of bootstrap for sampling without replacement from a finite population is proposed. This method can be used to estimate the variance in sampling with unequal inclusion probabilities and does not require artificial populations or utilization of bootstrap weights. The bootstrap samples are directly selected from the original sample. The bootstrap procedure contains two steps: in the first step, units are selected once with Poisson sampling using the same inclusion probabilities as the original design. In the second step, amongst the non-selected units, half of the units are randomly selected twice. This procedure enables us to efficiently estimate the variance. A set of simulations show the advantages of this new resampling method.

References

[1]
Antal E, Tillé Y (2011a) A direct bootstrap method for complex sampling designs from a finite population. J Am Stat Assoc 106:534-543.
[2]
Antal E, Tillé Y (2011b) Simple random sampling with over-replacement. J Stat Plan Inference 141:597-601.
[3]
Beaumont J-F, Patak Z (2012) On the generalized bootstrap for sample surveys with special attention to poisson sampling. Int Stat Rev 80(1):127-148.
[4]
Bertail P, Combris P (1997) Bootstrap généralisé d'un sondage. Annales d'Economie et de Statistique 46:49-83.
[5]
Booth JG, Butler RW, Hall P (1994) Bootstrap methods for finite populations. J Am Stat Assoc 89:1282-1289.
[6]
Brewer KRW, Donadio ME (2003) The high entropy variance of the Horvitz-Thompson estimator. Surv Methodol 29:189-196.
[7]
Brewer KRW, Hanif M (1983) Sampling with unequal probabilities. Springer, New York.
[8]
Chao MT, Lo SH (1985) A bootstrap method for finite population. Sankhy A 47:399-405.
[9]
Chauvet G (2007) Méthodes de bootstrap en population finie. PhD thesis, Université Rennes 2.
[10]
Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7:1-26.
[11]
Gross ST (1980) Median estimation in sample surveys. In: ASA proceedings of the section on survey research methods. American Statistical Association, pp 181-184.
[12]
Hájek J (1981) Sampling from a finite population. Marcel Dekker, New York.
[13]
Henderson T (2006) Estimating the variance of the Horvitz-Thompson estimator. Master's thesis, School of Finance and Applied Statistics, The Australian National University.
[14]
Holmberg A (1998) A bootstrap approach to probability proportional-to-size sampling. In: ASA proceedings of the section on survey research methods. American Statistical Association, pp 378-383.
[15]
Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. J Am Stat Assoc 47:663-685.
[16]
Kuk AYC (1989) Double bootstrap estimation of variance under systematic sampling with probability proportional to size. J Stat Comput Simul 31:73-82.
[17]
Lahiri P (2003) On the impact of bootstrap in survey sampling and small-area estimation. Stat Sci 18:199-210.
[18]
Mac Carthy PJ, Snowden CB (1985) The bootstrap and finite population sampling. Public Health Service Publication, Technical report.
[19]
Mason D, Newton MA (1992) A rank statistic approach to the consistency of a general bootstrap. Ann Stat 20:1611-1624.
[20]
Matei A, Tillé Y (2005) Evaluation of variance approximations and estimators in maximum entropy sampling with unequal probability and fixed sample size. J Off Stat 21(4):543-570.
[21]
Patak Z, Beaumont J-F (2009) Generalized bootstrap for prices surveys. In paper presented at the 57th Session of the International Statistical Institute, Durban, South-Africa.
[22]
Preston J, Henderson T (2007) Replicate variance estimation and high entropy variance approximations. In Papers presented at the ICES-III, June 18-21, 2007, Montreal, QC, Canada.
[23]
Rao JNK, Wu CFJ (1988) Resampling inference for complex survey data. J Am Stat Assoc 83:231-241.
[24]
Rao JNK, Wu CFJ, Yue K (1992) Some recent work on resampling methods for complex surveys. Surv Methodol 18:209-217.
[25]
Saigo H, Shao J, Sitter RR (2001) A repeated half-sample bootstrap and balanced repeated replications for randomly imputed data. Surv Methodol 27(2):189-196.
[26]
Särndal C-E, Swensson B, Wretman JH (1992) Model assisted survey sampling. Springer, New York.
[27]
Sen AR (1953) On the estimate of the variance in sampling with varying probabilities. J Indian Soc Agric Stat 5:119-127.
[28]
Shao J, Tu D (1995) The jacknife and bootstrap. Sprinter, New York.
[29]
Sitter RR (1992a) Comparing three bootstrap methods for survey data. Can J Stat 20:135-154.
[30]
Sitter RR (1992b) A resampling procedure for complex survey data. J Am Stat Assoc 87:755-765.
[31]
Tillé Y (2006) Sampling algorithms. Springer, New York.
[32]
Yates F, Grundy PM (1953) Selection without replacement from within strata with probability proportional to size. J R Stat Soc B15:235-261.
  1. A new resampling method for sampling designs without replacement: the doubled half bootstrap

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      Published In

      cover image Computational Statistics
      Computational Statistics  Volume 29, Issue 5
      October 2014
      491 pages
      ISSN:0943-4062
      EISSN:1613-9658
      Issue’s Table of Contents

      Publisher

      Kluwer Academic Publishers

      United States

      Publication History

      Published: 01 October 2014

      Author Tags

      1. Poisson sampling
      2. Simple random sampling
      3. Unequal probability sampling
      4. Variance estimation

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