rotations (version 1.0)

prentice: Eigenvector theory confidence region

Description

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 variability 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.

See Also

bayesCR, fisheretal, chang, zhang

Examples

Qs<-ruars(20, rcayley, kappa = 100, space = 'Q4')

#The prentice method can be accesed from the "region" function or the "prentice" function
region(Qs, method = 'eigen', type = 'theory', alp = 0.1, estimator='mean')
prentice(Qs, alp = 0.1)