are_nr {GeodRegr}

Newton-Raphson method for the are function

Description

Finds the positive multiplier of \sigma, 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.

Usage

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

Arguments

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.

Details

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.

Value

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

Author(s)

Ha-Young Shin

References

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

See Also

are.

Examples

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)