Find the radius of a $100(1-\alpha)$% confidence
region for the central orientation.
Usage
fisheretal(x, alp, boot, m, symm)
## S3 method for class 'Q4':
fisheretal(x, alp = NULL, boot = T,
m = 300, symm = TRUE)
## S3 method for class 'SO3':
fisheretal(x, alp = NULL, boot = T,
m = 300, symm = T)
Arguments
x
$n\times p$ matrix where each row
corresponds to a random rotation in matrix (p=9) or
quaternion (p=4) form.
alp
alpha level desired, e.g. 0.05 or 0.10.
boot
should the bootstrap or normal theory
critical value be used.
m
number of bootstrap replicates to use to
estimate critical value.
symm
logical; if TRUE (default), a symmetric
region is constructed.
Value
Radius of the confidence region centered at the projected
mean.
Details
Compute the radius of a $100(1-\alpha)$% confidence
region for the central orientation based on the projected
mean estimator using the method for the mean polar axis
as proposed in Fisher et al. (1996). To be able
to reduce their method to a radius requires the additional
assumption of rotational symmetry, equation (10) in
Fisher et al. (1996).
References
Fisher N, Hall P, Jing B and Wood A (1996). "Improved
pivotal methods for constructing confidence regions with
directional data." Journal of the American Statistical
Association, 91(435), pp. 1062-1070.