# rwild

##### Wild bootstrap residuals

The wild bootstrap residuals are computed as \(residuals*V\), where \(V\) is a sampling from a random variable (see details section).

- Keywords
- distribution

##### Usage

`rwild(residuals, type = "golden")`

##### Arguments

- residuals
residuals

- type
Type of distribution of V.

##### Details

For the construction of wild bootstrap residuals, sampling from a random variable \(V\) such that \(E[V^2]=0\) and \(E[V]=0\) is needed. A simple and suitable \(V\) is obtained with a discrete variable of the form:

``golden'', Sampling from golden section bootstrap values suggested by Mammen (1993). $$P\Bigg\{ V=\frac{1-\sqrt{5}}{2} \Bigg\} = \frac{5+\sqrt{5}}{10} \, and \, P\Bigg\{ V=\frac{1+\sqrt{5}}{2} \Bigg\} = \frac{5-\sqrt{5}}{10},$$ which leads to the

*golden section bootstrap*.``Rademacher'', Sampling from Rademacher distribution values \(\big\{-1,\,1\big\}\) with probabilities \(\big\{\frac{1}{2},\,\frac{1}{2}\big\}\), respectively.

``normal'', Sampling from a standard normal distribution.

##### Value

The wild bootstrap residuals computed using a sample of the random variable \(V\).

##### References

Mammen, E. (1993). *Bootstrap and wild bootstrap for high dimensional linear models*.
Annals of Statistics 21, 255 285.
Davidson, R. and E. Flachaire (2001). *The wild bootstrap, tamed at last*. working paper IER1000, Queens University.

##### See Also

##### Examples

```
# NOT RUN {
n<-100
# For golden wild bootstrap variable
e.boot0=rwild(rep(1,len=n),"golden")
# Construction of wild bootstrap residuals
e=rnorm(n)
e.boot1=rwild(e,"golden")
e.boot2=rwild(e,"Rademacher")
e.boot3=rwild(e,"normal")
summary(e.boot1)
summary(e.boot2)
summary(e.boot3)
# }
```

*Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2*