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) amongst 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.