rotations (version 0.1)

region: Confidence region for central orientation

Description

Find the radius of a $100(1-\alpha)$% confidence region for the central orientation based on the projected mean or median. For more on the currently available methods see prentice, fisheretal, chang, and zhang.

Usage

region(x, method, type, estimator, alp, ...)
  ## S3 method for class 'Q4':
region(x, method, type, estimator,
    alp = NULL, ...)
  ## S3 method for class 'SO3':
region(x, method, type, estimator,
    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.

method

character string specifying which type of interval to report, "eigen" or "moment" based theory.

type

character string, "bootstrap" or "theory" are available.

estimator

character string either "mean" or "median."

alp

the alpha level desired, e.g. 0.05 or 0.10.

...

additional arguments that are method specific.

Value

• Radius of the confidence region centered at the projected mean.

References

Prentice MJ (1986). "Orientation statistics without parametric assumptions." Journal of the Royal Statistical Society. Series B (Methodological), pp. 214-222.

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.

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.

Chang T and Rivest L (2001). "M-estimation for location and regression parameters in group models: A case study using Stiefel manifolds." Annals of Statistics, pp. 784-814.

See Also

prentice, fisheretal, chang, zhang

Examples

Rs<-ruars(20,rcayley,kappa=100)
region(Rs,method='eigen',type='theory',estimator='mean',alp=0.1)
region(Rs,method='eigen',type='bootstrap',estimator='mean',alp=0.1,symm=TRUE)
region(Rs,method='moment',type='bootstrap',estimator='mean',alp=0.1,m=100)
region(Rs,method='moment',type='theory',estimator='mean',alp=0.1)