are_nr: Newton-Raphson method for the 'are' function
In GeodRegr: Geodesic Regression

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/efficiency.R

Finds the positive multiplier of σ, the square root of the variance, used in the cutoff parameter that will give the desired (approximate) level of efficiency for the provided M-type estimator. Does so by using are and its partial derivative with respect to c in the Newton-Raphson method.

1	are_nr(estimator, n, startingpoint, level = 0.95)

`estimator`	M-type estimator (`'huber'` or `'tukey'`).
`n`	Dimension of the manifold.
`startingpoint`	Initial estimate for the Newton-Raphson method. May be determined after looking at a graph of the `are` function.
`level`	The desired ARE to the `'l2'` estimator.

As is often the case with the Newton-Raphson method, the starting point must be chosen carefully in order to ensure convergence. The use of the graph of the are function to find a starting point close to the root is recommended.

Positive multiplier of σ, the square root of the variance, used in the cutoff parameter, to give the desired level of efficiency.

Ha-Young Shin

Shin, H.-Y. and Oh H.-S. (2020). Robust Geodesic Regression. <arXiv:2007.04518>

are.

dimension <- 4
x <- 1:10000 / 1000
# use a graph of the are function to pick a good starting point
plot(x, are('huber', dimension, x) - 0.95)
are_nr('huber', dimension, 2)