objective_support: Internal function to minimize to compute the function sigma for the projections of the identified set

Description

Internal function to minimize to compute the function sigma for the projections of the identified set

Usage

objective_support(
  x,
  dir_nb,
  sam0,
  eps1,
  Xc_xb,
  Xncb,
  Xc_yb,
  Yb,
  values,
  grid,
  weights_x,
  weights_y,
  constraint,
  c_sign,
  nc_sign,
  refs0,
  meth = "adapt",
  T_xy,
  bc = FALSE,
  version = "first",
  R2bound = NULL,
  values_sel = NULL,
  ties = FALSE,
  modeNA = FALSE
)

Value

the value the support function

Arguments

x: value at which the function is evaluated.
dir_nb: the index of the considered direction.
sam0: the set of directions e where to compute the support function
eps1: the matrix of directions q, along the canonical axis, and the selected epsilon(q)
Xc_xb: the possibly bootstraped/subsampled common regressor on the dataset (Xnc,Xc). Default is NULL.
Xncb: the possibly bootstraped/subsampled noncommon regressor on the dataset (Xnc,Xc). No default.
Xc_yb: the possibly bootstraped/subsampled common regressor on the dataset (Y,Xc). Default is NULL.
Yb: the possibly bootstraped/subsampled outcome variable on the dataset (Y,Xc). No default.
values: the different unique points of support of the common regressor Xc.
grid: the number of points for the grid search on epsilon. Default is 30. If NULL, then epsilon is taken fixed equal to kp.
weights_x: the bootstrap or sampling weights for the dataset (Xnc,Xc).
weights_y: the bootstrap or sampling weights for the dataset (Y,Xc).
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.
refs0: indicating the positions in the vector values corresponding to the components of betac.
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".
T_xy: the apparent sample size the taking into account the difference in the two datasets.
bc: if TRUE compute also the bounds on betac. Default is FALSE.
version: version of the computation of the ratio, "first" is a degraded version but fast; "second" is a correct version but slower. Default is "second".
R2bound: the lower bound on the R2 of the long regression if any. Default is NULL.
values_sel: the selected values of Xc for the conditioning. Default is NULL.
ties: Boolean indicating if there are ties in the dataset. Default is FALSE.
modeNA: indicates if NA introduced if the interval is empty. Default is FALSE.