fisherCR: Fisher Mean Polax Axis CR Method

In heike/rotations: Tools for working with rotational data

Description

Find the radius of a 100(α)% confidence region for the projected mean Fisher et al. (1996)

Usage

  fisherCR(Qs, a, boot, m)

  ## S3 method for class 'Q4'
 fisherCR(Qs, a, boot = T, m = 300)

  ## S3 method for class 'SO3'
 fisherCR(Rs, a, boot = T, m = 300)

Arguments

Rs,Qs	A n-by-p matrix where each row corresponds to a random rotation in matrix (p=9) or quaternion form (p=4)
a	The alpha level desired, e.g. 0.95 or 0.90
boot	Should the bootstrap or normal theory critical value be used
m	number of bootstrap replicates to use to estimate critical value

Details

This works in the same way as done in Bingham et al. (2009) which assumes rotational symmetry and is therefore conservative.

Value

radius of the confidence region centered at the projected mean

References

Bingham M, Nordman D and 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.

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.

Examples

Qs<-ruars(20,rcayley,kappa=100,space='Q4')
region(Qs,method='fisher',alpha=0.9)

heike/rotations documentation built on May 17, 2019, 3:24 p.m.