bcanon {bootstrap} | R Documentation |

## Nonparametric BCa Confidence Limits

### Description

See Efron and Tibshirani (1993) for details on this function.

### Usage

```
bcanon(x, nboot, theta, ...,
alpha=c(0.025, 0.05, 0.1, 0.16, 0.84, 0.9, 0.95, 0.975))
```

### Arguments

`x` |
a vector containing the data. To bootstrap more complex data structures (e.g. bivariate data) see the last example below. |

`nboot` |
number of bootstrap replications |

`theta` |
function defining the estimator used in constructing the confidence points |

`...` |
additional arguments for |

`alpha` |
optional argument specifying confidence levels desired |

### Value

list with the following components

`confpoints` |
estimated bca confidence limits |

`z0` |
estimated bias correction |

`acc` |
estimated acceleration constant |

`u` |
jackknife influence values |

`call` |
The deparsed call |

### References

Efron, B. and Tibshirani, R. (1986). The Bootstrap Method for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, Vol 1., No. 1, pp 1-35.

Efron, B. (1987). Better bootstrap confidence intervals (with discussion). J. Amer. Stat. Assoc. vol 82, pg 171

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

### Examples

```
# bca limits for the mean
# (this is for illustration;
# since "mean" is a built in function,
# bcanon(x,100,mean) would be simpler!)
x <- rnorm(20)
theta <- function(x){mean(x)}
results <- bcanon(x,100,theta)
# To obtain bca limits for functions of more
# complex data structures, write theta
# so that its argument x is the set of observation
# numbers and simply pass as data to bcanon
# the vector 1,2,..n.
# For example, find bca limits for
# the correlation coefficient from a set of 15 data pairs:
xdata <- matrix(rnorm(30),ncol=2)
n <- 15
theta <- function(x,xdata){ cor(xdata[x,1],xdata[x,2]) }
results <- bcanon(1:n,100,theta,xdata)
```

*bootstrap*version 2019.6 Index]