rotations (version 1.5)

prentice: Transformation based asymptotic confidence region

Description

Find the radius of a $100(1-\alpha)$% confidence region for the projected mean based on a result from directional statistics.

Usage

prentice(x, alp)
  "prentice" (x, alp = NULL)
  "prentice" (x, alp = NULL)

Arguments

x

$n-by-p$ 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 M (1986). "Orientation statistics without parametric assumptions." Journal of the Royal Statistical Society. Series B (Methodological), 48(2), 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 = "transformation", type = "asymptotic", alp = 0.1, estimator = "mean")
prentice(Qs, alp = 0.1)