rotations (version 1.0)

fisheretal: Eigenvector theory pivotal bootstrap confidence region

Description

Find the radius of a $100(1-\alpha)$% confidence region for the central orientation based on eigenvector theory.

Usage

fisheretal(x, alp, boot, m, symm)
  ## S3 method for class 'Q4':
fisheretal(x, alp = NULL, boot = T,
    m = 300, symm = TRUE)
  ## S3 method for class 'SO3':
fisheretal(x, alp = NULL, boot = T,
    m = 300, symm = T)

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.

Value

• Radius of the confidence region centered at the projected mean.

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 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).

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.

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 = 'eigen', type = 'bootstrap', alp = 0.1, symm = TRUE, estimator = 'mean')
fisheretal(Qs, alp = 0.1, boot=TRUE, symm = TRUE)