## The Annals of Statistics

### Bootstrap and Wild Bootstrap for High Dimensional Linear Models

Enno Mammen

#### Abstract

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.

#### Article information

Source
Ann. Statist. Volume 21, Number 1 (1993), 255-285.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176349025

JSTOR

Digital Object Identifier
doi:10.1214/aos/1176349025

Zentralblatt MATH identifier
0771.62032

Mathematical Reviews number (MathSciNet)
MR1212176

Subjects
Primary: 62G09: Resampling methods
Secondary: 62F10: Point estimation 62F12: Asymptotic properties of estimators

#### Citation

Mammen, Enno. Bootstrap and Wild Bootstrap for High Dimensional Linear Models. Ann. Statist. 21 (1993), no. 1, 255--285. doi:10.1214/aos/1176349025. http://projecteuclid.org/euclid.aos/1176349025.