Compute initial estimates for the EN S-estimator using the EN-PY procedure.

enpy_initial_estimates(
  x,
  y,
  alpha,
  lambda,
  bdp = 0.25,
  cc,
  intercept = TRUE,
  penalty_loadings,
  enpy_opts = enpy_options(),
  mscale_opts = mscale_algorithm_options(),
  eps = 1e-06,
  sparse = FALSE,
  ncores = 1L
)

Arguments

x

n by p matrix of numeric predictors.

y

vector of response values of length n.

alpha

elastic net penalty mixing parameter with \(0 \le \alpha \le 1\). alpha = 1 is the LASSO penalty, and alpha = 0 the Ridge penalty. Can be a vector of several values, but alpha = 0 cannot be mixed with other values.

lambda

a vector of positive values of penalization levels.

bdp

desired breakdown point of the estimator, between 0 and 0.5. The actual breakdown point may be slightly larger/smaller to avoid instabilities of the S-loss.

cc

cutoff value for the bisquare rho function. By default, chosen to yield a consistent estimate for the Normal distribution.

intercept

include an intercept in the model.

penalty_loadings

a vector of positive penalty loadings (a.k.a. weights) for different penalization of each coefficient. Only allowed for alpha > 0.

enpy_opts

options for the EN-PY algorithm, created with the enpy_options() function.

mscale_opts

options for the M-scale estimation. See mscale_algorithm_options() for details.

eps

numerical tolerance.

sparse

use sparse coefficient vectors.

ncores

number of CPU cores to use in parallel. By default, only one CPU core is used. Not supported on all platforms, in which case a warning is given.

Details

If these manually computed initial estimates are intended as starting points for pense(), they are by default shared for all penalization levels. To restrict the use of the initial estimates to the penalty level they were computed for, use as_starting_point(..., specific = TRUE). See as_starting_point() for details.

References

Cohen Freue, G.V.; Kepplinger, D.; Salibián-Barrera, M.; Smucler, E. Robust elastic net estimators for variable selection and identification of proteomic biomarkers. Ann. Appl. Stat. 13 (2019), no. 4, 2065--2090 doi: 10.1214/19-AOAS1269

See also

Other functions for initial estimates: prinsens(), starting_point()