rotations (version 1.0)

chang: M-estimator theory confidence region

Description

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

Usage

chang(x, estimator, alp)
  ## S3 method for class 'SO3':
chang(x, estimator, alp = NULL)
  ## S3 method for class 'Q4':
chang(x, estimator, alp = NULL)

Arguments

x

$n\times p$ matrix where each row corresponds to a random rotation in matrix ($p=9$) or quaternion ($p=4$) form.

estimator

character string either "mean" or "median."

alp

alpha level desired, e.g. 0.05 or 0.10.

Value

• Radius of the confidence region centered at the specified estimator.

Details

Compute the radius of a $100(1-\alpha)$% confidence region for the central orientation centered at the projected mean or median based on a result due to Chang et al. (2001) among others. By construction each axis will have the same radius so the radius reported is for all three axes.

References

Chang T and Rivest L (2001). "M-estimation for location and regression parameters in group models: A case study using Stiefel manifolds." _Annals of statistics_, pp. 784-814.

See Also

bayesCR, prentice, fisheretal, zhang

Examples

Rs <- ruars(20, rcayley, kappa = 100)

#The chang method can be accesed from the "region" function or the "chang" function
region(Rs, method = 'moment', type = 'theory', alp = 0.1, estimator = 'mean')
chang(Rs, estimator = 'mean', alp = 0.1)