zhang {rotations} | R Documentation |
M-estimator theory pivotal bootstrap confidence region
Description
Compute the radius of a 100(1-\alpha)
% confidence region for the
central orientation based on M-estimation theory.
Usage
zhang(x, estimator, alp = NULL, m = 300)
## 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 |
|
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 estimate the critical value. |
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due to Zhang & Nordman (2009) (unpublished MS thesis).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. This
method is called "direct" because it used M-estimation theory for SO(3)
directly instead of relying on transforming a result from directional
statistics as prentice
and fisheretal
do.
Value
Radius of the confidence region centered at the specified estimator.
See Also
bayesCR
, prentice
,
fisheretal
, chang
Examples
Rs <- ruars(20, rcayley, kappa = 100)
# The zhang method can be accesed from the "region" function or the "zhang" function
# They will be different because it is a bootstrap.
region(Rs, method = "direct", type = "bootstrap", alp = 0.1, estimator = "mean")
zhang(Rs, estimator = "mean", alp = 0.1)