Pauly, Markus Consistency of the subsample bootstrap empirical process. (English) Zbl 1316.62055 Statistics 46, No. 5, 621-626 (2012). Summary: In the classical bootstrap approach the number of distinct observation in the resample is random. To overcome this hitch C. R. Rao et al. [J. Stat. Plann. Inference 64, No. 2, 257–281 (1997; Zbl 0945.62014)] have proposed a modified resampling procedure – the so-called Sequential Bootstrap or 0.632-Bootstrap – in which each resample has exactly the same number \(m \simeq \lfloor 0.632n \rfloor\) of distinct observations. Motivated by this idea we introduce an akin procedure, the subsample bootstrap, where additionally even the size of each resample is equal. It will turn out that the subsample bootstrap empirical process is consistent for a wide class of Donsker classes. Cited in 8 Documents MSC: 62G09 Nonparametric statistical resampling methods 62L10 Sequential statistical analysis 62G20 Asymptotic properties of nonparametric inference Keywords:bootstrap; sequential bootstrap; empirical process; Donsker classes; resampling methods Citations:Zbl 0945.62014 PDFBibTeX XMLCite \textit{M. Pauly}, Statistics 46, No. 5, 621--626 (2012; Zbl 1316.62055) Full Text: DOI References: [1] DOI: 10.1016/S0378-3758(97)00041-4 · Zbl 0945.62014 · doi:10.1016/S0378-3758(97)00041-4 [2] DOI: 10.1080/01621459.1983.10477973 · doi:10.1080/01621459.1983.10477973 [3] DOI: 10.1081/STA-100105691 · Zbl 1097.62548 · doi:10.1081/STA-100105691 [4] Babu, G. J., Pathak, P. K. and Rao, C. R. 2000.Consistency and Accuracy of the Sequential Bootstrap, 21–31. New York: Dekker. Statistics for the 21th century by C.R. Rao · Zbl 1022.62067 [5] DOI: 10.1214/aos/1176351062 · Zbl 0655.62031 · doi:10.1214/aos/1176351062 [6] DOI: 10.1007/978-1-4612-2950-6 · doi:10.1007/978-1-4612-2950-6 [7] Nguyen Van Toan, Vietnam J. Math. 33 pp 261– (2005) [8] DOI: 10.1016/j.spl.2005.10.038 · Zbl 1090.62042 · doi:10.1016/j.spl.2005.10.038 [9] DOI: 10.1214/aos/1176348787 · Zbl 0777.62045 · doi:10.1214/aos/1176348787 [10] Van der Vaart A. W., Weak Convergence and Empirical Processes (1995) · Zbl 0809.62040 [11] Johnson N., Urn Models and Their Application (1977) [12] DOI: 10.1214/aop/1176989011 · Zbl 0792.62038 · doi:10.1214/aop/1176989011 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.