fisheretal {rotations}

Transformation based pivotal bootstrap confidence region

Description

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

Usage

fisheretal(x, alp = NULL, boot = TRUE, m = 300, symm = TRUE)

## 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\times 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-\alpha)% confidence region for the central orientation based on the projected mean estimator using the method for the mean polar axis as proposed in fisher1996. To be able to reduce their method to a radius requires the additional assumption of rotational symmetry, equation (10) in fisher1996.

fisher1996

Value

Radius of the confidence region centered at the projected mean.

See Also

bayesCR, prentice, chang, zhang

Examples

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)