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March, 1993 Bootstrap and Wild Bootstrap for High Dimensional Linear Models
Enno Mammen
Ann. Statist. 21(1): 255-285 (March, 1993). DOI: 10.1214/aos/1176349025


In this paper 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 $n\rightarrow\infty$. 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.


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Enno Mammen. "Bootstrap and Wild Bootstrap for High Dimensional Linear Models." Ann. Statist. 21 (1) 255 - 285, March, 1993.


Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0771.62032
MathSciNet: MR1212176
Digital Object Identifier: 10.1214/aos/1176349025

Primary: 62G09
Secondary: 62F10 , 62F12

Keywords: bootstrap , dimension asymptotics , linear models , wild bootstrap

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 1 • March, 1993
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