# fisheretal: Transformation based pivotal bootstrap confidence region In rotations: Tools for Working with Rotation Data

## Description

Find the radius of a 100(1-α)% confidence region for the central orientation based on transforming a result from directional statistics.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ``` fisheretal(x, alp, boot, m, symm) ## S3 method for class 'Q4' fisheretal(x, alp = NULL, boot = TRUE, m = 300, symm = TRUE) ## S3 method for class 'SO3' fisheretal(x, alp = NULL, boot = TRUE, m = 300, symm = TRUE) ```

## Arguments

 `x` n-by-p matrix where each row corresponds to a random rotation in matrix (p=9) or quaternion (p=4) form. `alp` alpha level desired, e.g. 0.05 or 0.10. `boot` should the bootstrap or normal theory critical value be used. `m` number of bootstrap replicates to use to estimate critical value. `symm` logical; if TRUE (default), a symmetric region is constructed.

## Details

Compute the radius of a 100(1-α)% confidence region for the central orientation based on the projected mean estimator using the method for the mean polar axis as proposed in Fisher et al. (1996). To be able to reduce their method to a radius requires the additional assumption of rotational symmetry, equation (10) in Fisher et al. (1996).

## Value

Radius of the confidence region centered at the projected mean.

## References

Fisher N, Hall P, Jing B and Wood A (1996). "Improved pivotal methods for constructing confidence regions with directional data." Journal of the American Statistical Association, 91(435), pp. 1062-1070.

`bayesCR`, `prentice`, `chang`, `zhang`
 ```1 2 3 4 5 6``` ```Qs<-ruars(20, rcayley, kappa = 100, space = 'Q4') #The Fisher et al. method can be accesed from the "region" function or the "fisheretal" function region(Qs, method = "transformation", type = "bootstrap", alp = 0.1, symm = TRUE, estimator = "mean") fisheretal(Qs, alp = 0.1, boot = TRUE, symm = TRUE) ```