## Confidence Interval for the Median Absolute Deviation

### Description

This function calculates bootstrap confidence intervals for the population median absolute deviation, see stats::mad for more information on this measure of scale.

### Usage

ci_mad(
x,
probs = c(0.025, 0.975),
constant = 1.4826,
type = "bootstrap",
boot_type = c("bca", "perc", "norm", "basic"),
R = 9999,
seed = NULL,
...
)


### Arguments

 x A numeric vector. probs Error probabilites. The default c(0.025, 0.975) gives a symmetric 95% confidence interval. constant Scaling factor applied. The default (1.4826) ensures that the MAD equals the standard deviation for a theoretical normal distribution. type Type of confidence interval. Currently not used as the only type is "bootstrap". boot_type Type of bootstrap confidence interval c("bca", "perc", "norm", "basic"). R The number of bootstrap resamples. seed An integer random seed. ... Further arguments passed to boot::boot.

### Details

Bootstrap confidence intervals are calculated by the package "boot", see references. The default bootstrap type is "bca" (bias-corrected accelerated) as it enjoys the property of being second order accurate as well as transformation respecting (see Efron, p. 188).

### Value

A list with class cint containing these components:

• parameter: The parameter in question.

• interval: The confidence interval for the parameter.

• estimate: The estimate for the parameter.

• probs: A vector of error probabilities.

• type: The type of the interval.

• info: An additional description text for the interval.

### References

1. Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.

2. Canty, A and Ripley B. (2019). boot: Bootstrap R (S-Plus) Functions.

### Examples

set.seed(1)
x <- rnorm(100)