select_epsilon: Function for the data-driven selection of the epsilon tuning parameter

Description

Function for the data-driven selection of the epsilon tuning parameter

Usage

select_epsilon(
  sam1,
  eps_default,
  Xc_x,
  Xnc,
  Xc_y,
  Y,
  values,
  dimXc,
  dimXnc,
  nb_pts,
  lim,
  weights_x,
  weights_y,
  refs0,
  grid = 30,
  constraint = NULL,
  c_sign = NULL,
  nc_sign = NULL,
  meth = "adapt",
  nbCores = 1,
  version_sel = "first",
  alpha = 0.05,
  ties = FALSE
)

Value

a matrix containing the values of the selected epsilon(q) for q directions in sam1.

Arguments

sam1: the matrix containing the directions q on which to compute the selected rule for epsilon(q)
eps_default: If grid =NULL, then epsilon is taken equal to eps_default.
Xc_x: the common regressor on the dataset (Xnc,Xc). Default is NULL.
Xnc: the noncommon regressor on the dataset (Xnc,Xc). No default.
Xc_y: the common regressor on the dataset (Y,Xc). Default is NULL.
Y: the outcome variable. No default.
values: the different unique points of support of the common regressor Xc.
dimXc: the dimension of the common regressors Xc.
dimXnc: the dimension of the noncommon regressors Xnc.
nb_pts: the constant C in DGM for the epsilon_0, the lower bound on the grid for epsilon, taken equal to nb_pts*ln(n)/n. Default is 1 without regressors Xc, 3 with Xc.
lim: the lim number of observations under which we do no compute the conditional variance.
weights_x: the sampling weights for the dataset (Xnc,Xc).
weights_y: the sampling weights for the dataset (Y,Xc).
refs0: indicating the positions in the vector values corresponding to the components of betac.
grid: the number of points for the grid search on epsilon. Default is 30. If NULL, then epsilon is taken fixed equal to eps_default.
constraint: a vector indicating the different constraints in a vector of the size of X_c indicating the type of constraints, if any on f(X_c) : "concave", "concave", "nondecreasing", "nonincreasing", "nondecreasing_convex", "nondecreasing_concave", "nonincreasing_convex", "nonincreasing_concave", or NULL for none. Default is NULL, no contraints at all.
c_sign: sign restrictions on the commonly observed regressors: -1 for a minus sign, 1 for a plus sign, 0 otherwise. Default is NULL, i.e. no constraints.
nc_sign: sign restrictions on the non-commonly observed regressors Xnc: -1 for a minus sign, 1 for a plus sign, 0 otherwise. Default is NULL, i.e. no constraints.
meth: the method for the choice of epsilon, either "adapt", i.e. adapted to the direction or "min" the minimum over the directions. Default is "adapt".
nbCores: number of cores for the parallel computation. Default is 1.
version_sel: version of the selection of the epsilon, "first" indicates no weights, no ties, same sizes of the two datasets; "second" otherwise. Default is "second".
alpha: the level for the confidence regions. Default is 0.05.
ties: Boolean indicating if there are ties in the dataset. Default is FALSE.