zbMATH — the first resource for mathematics

Applying the rescaling bootstrap under imputation: a simulation study. (English) Zbl 07193744
Summary: Resampling methods are a common measure to estimate the variance of a statistic of interest when data consist of nonresponse and imputation is used as compensation. Applying resampling methods usually means that subsamples are drawn from the original sample and that variance estimates are computed based on point estimators of several subsamples. However, newer resampling methods such as the rescaling bootstrap of J. Chipperfield and J. Preston [“Efficient bootstrap for business surveys”, Surv. Methodol. 33, No. 2, 167–172 (2007)] include all elements of the original sample in the computation of its point estimator. Thus, procedures to consider imputation in resampling methods cannot be applied in the ordinary way. For such methods, modifications are necessary. This paper presents an approach applying newer resampling methods for imputed data. The Monte Carlo simulation study conducted in the paper shows that the proposed approach leads to reliable variance estimates in contrast to other modifications.
62 Statistics
Full Text: DOI
[1] Mashreghi Z, Leger C, Haziza D.Bootstrap methods for imputed data from regression, ratio and hot-deck imputation. Canad J Stat. 2014;42(1):142-167. doi: 10.1002/cjs.11206[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1349.62027
[2] Shao J, Sitter R.Bootstrap for imputed survey data. J Am Stat Assoc. 1996;91(435):1278-1288. doi: 10.1080/01621459.1996.10476997[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0880.62011
[3] Rao J, Shao J.Jackknife variance estimation with survey data under hot deck imputation. Biometrika. 1992;79(4):811-822. doi: 10.1093/biomet/79.4.811[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0764.62008
[4] Shao J, Chen Y, Chen Y.Balanced repeated replication for stratified multistage survey data under imputation. J Am Stat Assoc. 1998;93(442):819-831. doi: 10.1080/01621459.1998.10473733[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0947.62010
[5] Chipperfield J, Preston J.Efficient bootstrap for business surveys. Surv Methodol. 2007;33:167-172. [Web of Science ®], [Google Scholar]
[6] Shao J, Tu D. The jackknife and bootstrap. New York: Springer; 1995. [Crossref], [Google Scholar] · Zbl 0947.62501
[7] Davison AC, Sardy S. Resampling methods for variance estimation. Workpackage 5. Deliverable 5.1. Dacseis Project; 2004. Available from: https://www.uni-trier.de/index.php?id=29730. [Google Scholar]
[8] Wolter KM. Introduction to variance estimation. New York: Springer; 2007. [Google Scholar] · Zbl 1284.62023
[9] Shao J. Replication methods for variance estimation in complex surveys with imputed data. In: Groves R. M., Dillman D. A., Eltinge J. L., et al., editors. Survey Nonresponse. New-York: Wiley; 2002. p. 303-314. [Google Scholar]
[10] Preston J.Rescaled bootstrap for stratified multistage sampling. Surv Methodol. 2009;35:227-234. [Web of Science ®], [Google Scholar]
[11] Bruch C. Varianzschätzung unter Imputation und bei komplexen Stichprobendesigns [Variance estimation under imputation and for complex sampling designs] [dissertation]. Trier University; 2016. Available from: http://ubt.opus.hbz-nrw.de/volltexte/2016/1009/. [Google Scholar]
[12] R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna; 2014. Available from: https://www.R-project.org/. [Google Scholar]
[13] Genz A, Bretz F, Miwa T, et al. mvtnorm: Multivariate Normal and t Distributions. R package version 1.0-2; 2014. Available from: http://CRAN.R-project.org/package=mvtnorm. [Google Scholar]
[14] Van den Boogaart KG, Tolosana R, Bren M. compositions Compositional Data Analysis. R package version 1.40-1; 2014. Available from: http://CRAN.R-project.org/package=compositions. [Google Scholar]
[15] Genz A, Bretz B. Computation of multivariate normal and t probabilities. Heidelberg: Springer-Verlag; 2009. (Lecture Notes in Statistics; 195). [Crossref], [Google Scholar] · Zbl 1204.62088
[16] Burgard JP, Kolb J-P, Münnich R, et al. Synthetic data for open and reproducible methodological research in social sciences and official statistics. AStA Wirtschafts- und Sozialstatistisches Archiv. 2017;11(3-4):233-244. doi: 10.1007/s11943-017-0214-8[Crossref], [Google Scholar]
[17] Burgard JP, Ertz F, Merkle H, et al. AMELIA - data description v0.2.2.1; 2017. Available from: http://amelia.uni-trier.de/?p=173. [Google Scholar]
[18] Alfons A, Filzmoser P, Hulliger B, et al. Synthetic data generation of SILC data. Deliverable D6.2.AMELI project; 2011. Available from: https://www.uni-trier.de/index.php?id=24676&L=2. [Google Scholar]
[19] Kolb J-P. Methoden zur Erzeugung synthetischer Simulationsgesamtheiten [dissertation]. Trier University; 2012. Available from: http://ubt.opus.hbz-nrw.de/volltexte/2013/816/. [Google Scholar]
[20] Enderle T, Münnich R, Bruch C.On the impact of response patterns on survey estimates from access panels. Surv Res Methods. 2013;7:91-101. [Web of Science ®], [Google Scholar]
[21] Fay RE. A design-based perspective on missing data variance. Proceedings of the 1991 Annual Research Conference. U.S. Bureau of the Census; 1991; p. 429-440. [Google Scholar]
[22] Shao J, Steel P.Variance estimation for survey data with composite imputation and nonnegligible sampling fractions. J Am Stat Assoc. 1999;94(445):254-265. doi: 10.1080/01621459.1999.10473841[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1072.62518
[23] Saigo H, Shao J, Sitter R.A repeated half-sample bootstrap and balanced repeated replications for randomly imputed data. Surv Methodol. 2001;27(2):189-196. [Google Scholar]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.