zhang: M-estimator theory pivotal boostrap confidence region
Description
Compute the radius of a $100(1-\alpha)$% confidence
region for the central orientation based on M-estiamtor
theory.
Usage
zhang(x, estimator, alp, m)
## S3 method for class 'SO3':
zhang(x, estimator, alp = NULL, m = 300)
## S3 method for class 'Q4':
zhang(x, estimator, alp = NULL, m = 300)
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.
m
number of replicates to use to estiamte the
critical value.
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 based on the projected
mean estimator using the method due to Zhang & Nordman
(2009) (unpublished MS thesis). By construction each
axis will have the same radius so the radius reported is
for all three axis. A normal theory version of this
procedure uses the theoretical chi-square limiting
distribution and is given by the chang
option.