Find the radius of a $100(1-\alpha)$% confidence
region for the projected mean based on eigenvector based
result.
Usage
prentice(x, alp)
## S3 method for class 'Q4':
prentice(x, alp = NULL)
## S3 method for class 'SO3':
prentice(x, 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.
alp
alpha level desired, e.g. 0.05 or 0.10.
Value
Radius of the confidence region centered at the projected
mean for each of the x-, y- and z-axes.
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 Prentice
(1986). For a rotation specific version see
Rancourt et al. (2000). The variablity in each
axis is different so each axis will have its own radius.
References
Prentice MJ (1986). "Orientation statistics without
parametric assumptions." Journal of the Royal
Statistical Society. Series B (Methodological), pp.
214-222.
Rancourt D, Rivest L and Asselin J (2000). "Using
orientation statistics to investigate variations in human
kinematics." Journal of the Royal Statistical Society:
Series C (Applied Statistics), 49(1), pp. 81-94.