Politis, Dimitris N.; Romano, Joseph P.; Wolf, Michael On the asymptotic theory of subsampling. (English) Zbl 1006.62019 Stat. Sin. 11, No. 4, 1105-1124 (2001). Summary: A general approach to constructing confidence intervals by subsampling was presented by D.N. Politis and J.P. Romano [Ann. Stat. 22, No. 4, 2031-2050 (1994; Zbl 0828.62044)]. The crux of the method is recomputing a statistic over subsamples of the data, and these recomputed values are used to build up an estimated sampling distribution. The method works under extremely weak conditions, it applies to independent, identically distributed (i.i.d.) observations as well as to dependent data situations, such as time series (possibly nonstationary), random fields, and marked point processes. We present some theorems showing: a new construction for confidence intervals that removes a previous condition, a general theorem showing the validity of subsampling for data-dependent choices of the block size, and a general theorem for the construction of hypothesis tests (not necessarily derived from a confidence interval construction). The arguments apply to both the i.i.d. setting and the dependent data case. Cited in 16 Documents MSC: 62F25 Parametric tolerance and confidence regions 62G20 Asymptotic properties of nonparametric inference 62G10 Nonparametric hypothesis testing 62F03 Parametric hypothesis testing 62G15 Nonparametric tolerance and confidence regions 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:confidence intervals; data-dependent block size choice; large sample theory; resampling Citations:Zbl 0828.62044 PDFBibTeX XMLCite \textit{D. N. Politis} et al., Stat. Sin. 11, No. 4, 1105--1124 (2001; Zbl 1006.62019)