rotations (version 0.1)

prentice: Prentice confidence region method

Description

Find the radius of a $100(1-\alpha)$% confidence region for the projected mean.

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 variability in each axis is different so each axis will have its own radius. In Bingham et al. (2009) they take the largest radius and use it to form regions that are symmetric about all three axes.

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.

Bingham, M. A., Nordman, D., & Vardeman, S. (2009). "Modeling and inference for measured crystal orientations and a tractable class of symmetric distributions for rotations in three dimensions." Journal of the American Statistical Association, 104(488), pp. 1385-1397.

See Also

fisheretal, chang, zhang

Examples

Qs<-ruars(20,rcayley,kappa=100,space='Q4')
region(Qs,method='eigen',type='theory',alp=0.1,estimator='mean')