dot-find_stable_bdb_bisquare: Determine a breakdown point with stable numerical properties...

In pense: Penalized Elastic Net S/MM-Estimator of Regression

Determine a breakdown point with stable numerical properties of the M-scale with Tukey's bisquare rho function.

Description

The M-scale objective (and hence the S-loss) can have unbounded or very high 1st derivative. This can lead to numerical instability of the algorithms and in turn excessive computation time. This function chooses the breakdown point with lowest upper bound of the 1st derivative from a range of bdp's in the vicinity of the desired bdp.

Usage

.find_stable_bdb_bisquare(
  n,
  desired_bdp,
  tolerance = 0.01,
  precision = 1e-04,
  interval = c(0.05, 0.5)
)

Arguments

n	number of observations in the sample
desired_bdp	the desired breakdown point (between 0.05 and 0.5)
tolerance	how far can the chosen bdp be away from the desired bdp. The chosen bdp is guaranteed to be in the range given by interval.
precision	granularity of the grid of considered bdp's.
interval	restrict the chosen bdp to this interval.

pense documentation built on Feb. 16, 2023, 9:36 p.m.