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Consistency of the subsample bootstrap empirical process. (English) Zbl 1316.62055

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.

MSC:

62G09 Nonparametric statistical resampling methods
62L10 Sequential statistical analysis
62G20 Asymptotic properties of nonparametric inference

Citations:

Zbl 0945.62014
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References:

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