rotations (version 1.5)

chang: M-estimator asymptotic confidence region

Description

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

Usage

chang(x, estimator, alp)
  "chang" (x, estimator, alp = NULL)
  "chang" (x, estimator, alp = NULL)

Arguments

x

$n-by-p$ 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. This method is called "direct" because it uses M-estimation theory for SO(3) directly instead of relying on the transformation of a result from directional statistics like prentice and fisheretal do.

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, 29(3), 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 = "direct", type = "asymptotic", alp = 0.1, estimator = "mean")
chang(Rs, estimator = "mean", alp = 0.1)