zhang {rotations}R Documentation

M-estimator theory pivotal bootstrap confidence region

Description

Compute the radius of a 100(1-\alpha)% confidence region for the central orientation based on M-estimation theory.

Usage

zhang(x, estimator, alp = NULL, m = 300)

## S3 method for class 'SO3'
zhang(x, estimator, alp = NULL, m = 300)

## S3 method for class 'Q4'
zhang(x, estimator, alp = NULL, m = 300)

Arguments

x

n\times p matrix where each row corresponds to a random rotation in matrix (p=9) or quaternion (p=4) form.

estimator

character string either "mean" or "median."

alp

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

m

number of replicates to use to estimate the critical value.

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for the central orientation based on the projected mean estimator using the method due to Zhang & Nordman (2009) (unpublished MS thesis). By construction each axis will have the same radius so the radius reported is for all three axis. A normal theory version of this procedure uses the theoretical chi-square limiting distribution and is given by the chang option. This method is called "direct" because it used M-estimation theory for SO(3) directly instead of relying on transforming a result from directional statistics as prentice and fisheretal do.

Value

Radius of the confidence region centered at the specified estimator.

See Also

bayesCR, prentice, fisheretal, chang

Examples

Rs <- ruars(20, rcayley, kappa = 100)

# The zhang method can be accesed from the "region" function or the "zhang" function
# They will be different because it is a bootstrap.
region(Rs, method = "direct", type = "bootstrap", alp = 0.1, estimator = "mean")
zhang(Rs, estimator = "mean", alp = 0.1)

[Package rotations version 1.6.5 Index]