README.Rmd

---
title: "Fast and Robust Bootstrap"
author: "Matias Salibian"
date: "`r format(Sys.Date())`"
output: github_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning=FALSE)
```

## Fast and Robust Bootstrap

This package implements the Fast and Robust Bootstrap as proposed in 
[Salibian-Barrera and Zamar (2002)](http://dx.doi.org/10.1214/aos/1021379865), and
[Salibian-Barrera, M., Van Aels, S. and Willems, G. (2008)](http://dx.doi.org/10.1007/s10260-007-0048-6) for robust regression estimators (MM-estimators) computed with 
`robustbase::lmrob`. 

To install it use the following commands (assuming that you have
the `devtools` package from [CRAN](https://cran.r-project.org) 
already installed): 
```R
devtools::install_github("msalibian/FRB")
```
To use it (after installation), simply call `frb` on an `lmrob` object as computed 
by `robustbase::lmrob`. Here's an example:
```{R howtouse}
library(robustbase)
library(FRB)
a <- lmrob(LNOx ~ LNOxEm + sqrtWS, data=NOxEmissions)
set.seed(123)
tmp <- frb(lmrob.object=a, nboot=1000, return.coef=FALSE)
```

If the argument `return.coef` is set to `FALSE`, then
`frb` returns the estimated covariance matrix of the
robust regression estimators. For example, the
estimated standard errors for each parameter estimate
are
```{R ses}
sqrt(diag(tmp$var))
```
We can compare them with the 
estimated standard errors given by the usual
asyptotic approximation:
```{R asymp}
sqrt(diag(summary(a)$cov))
```

If the argument `return.coef` is `TRUE` then 
the returned list has an element `$coef` 
that contains a matrix with `nboot` rows
with a bootstrapped regression coefficient in 
each of them. 

The argument `return.indices` indicates whether
to return 
the matrix of the indices of the bootstrap samples. 

The argument `centered` indicates whether the
returned bootstrap regression coefficients 
should be centered ($\hat{\beta}^* - \hat{\beta}_n$)
or not. For example:
```{r centering}
# by default the bootstrapped estimators are centered
set.seed(123)
tmp <- frb(lmrob.object=a, nboot=1000, return.coef=TRUE)

# we now add the regression estimator to each bootstrapped one
tmp2 <- scale(tmp$coef, scale=FALSE, center=-coef(a))

# use the argument centered=FALSE to return the non-centered 
# bootstrapped estimators instead
set.seed(123)
tmp3 <- frb(lmrob.object=a, nboot=1000, return.coef=TRUE, centered=FALSE)

# and check that the results are the same
all.equal(tmp2, tmp3$coef)
```