Mammen, Enno Bootstrap and wild bootstrap for high dimensional linear models. (English) Zbl 0771.62032 Ann. Stat. 21, No. 1, 255-285 (1993). Summary: Two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of \(F\)-test statistics in high dimensional linear models. An asymptotic approach will be chosen where the dimension \(p\) of the model may increase for sample size \(n\to \infty\). The range of validity will be compared for the normal approximation and for the bootstrap procedures. Furthermore, it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework. This is in contrast to the usual asymptotic approach where \(p\) is fixed. Cited in 193 Documents MSC: 62G09 Nonparametric statistical resampling methods 62F12 Asymptotic properties of parametric estimators 62J05 Linear regression; mixed models 62E20 Asymptotic distribution theory in statistics Keywords:least squares estimates; wild bootstrap; dimension asymptotics; consistency; accuracy; bootstrap procedures; distribution of linear contrasts; \(F\)-test statistics; high dimensional linear models; asymptotic approach; normal approximation; rates of convergence PDFBibTeX XMLCite \textit{E. Mammen}, Ann. Stat. 21, No. 1, 255--285 (1993; Zbl 0771.62032) Full Text: DOI