DGM_bounds_test {RegCombin}

This function compute the DGM bounds for all the different coefficients, adapted to the point identification test.

Description

This function compute the DGM bounds for all the different coefficients, adapted to the point identification test.

Usage

DGM_bounds_test(
  Ldata,
  Rdata,
  values,
  sam0,
  refs0,
  out_var,
  nc_var,
  c_var = NULL,
  constraint = NULL,
  nc_sign = NULL,
  c_sign = NULL,
  nbCores = 1,
  eps_default = 0.5,
  nb_pts = 1,
  Bsamp = 1000,
  grid = 30,
  weights_x = NULL,
  weights_y = NULL,
  outside = FALSE,
  meth = "adapt",
  modeNA = FALSE,
  version = "first",
  version_sel = "first",
  alpha = 0.05,
  projections = FALSE,
  R2bound = NULL,
  values_sel = NULL,
  ties = FALSE,
  seed = 2131
)

Arguments

Ldata

dataset containing (Y,Xc) where Y is the outcome, Xc are potential common regressors.

Rdata

dataset containing (Xnc,Xc) where Xnc are the non commonly observed regressors, Xc are potential common regressors.

values

the different unique points of support of the common regressor Xc.

sam0

the directions q to compute the radial function.

refs0

indicating the positions in the vector values corresponding to the components of betac.

out_var

label of the outcome variable Y.

nc_var

label of the non commonly observed regressors Xnc.

c_var

label of the commonly observed regressors 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.

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.

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.

nbCores

number of cores for the parallel computation. Default is 1.

eps_default

If grid =NULL, then epsilon is taken equal to eps_default.

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.

Bsamp

the number of bootstrap/subsampling replications. Default is 1000.

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 sampling weights for the dataset (Xnc,Xc). Default is NULL.

weights_y

the sampling weights for the dataset (Y,Xc). Default is NULL.

outside

if TRUE indicates that the parallel computing has been launched outside of the function. Default is FALSE.

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".

modeNA

indicates if NA introduced if the interval is empty. Default is FALSE.

version

version of the computation of the ratio, "first" indicates no weights, no ties, same sizes of the two datasets; "second" otherwise. Default is "second".

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

for the level of the confidence region. Default is 0.05.

projections

if FALSE compute the identified set along some directions or the confidence regions. Default is FALSE

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.

seed

set a seed to fix the subsampling replications.

Value

a list containing, in order: - ci : a list with all the information on the confidence intervals

* upper: upper bound of the confidence interval on the radial function S in the specified direction at level alpha, possibly with sign constraints

* lower: lower bound upper bound of the confidence interval on the radial function S, possibly with sign constraints

* unconstr: confidence interval on the radial function S, without sign constraints

* If common regressors, upper_agg, lower_agg, and unconstr_agg reports the same values but aggregated over the values of Xc (see the parameter theta0 in the paper)

* betac_ci: confidence intervals on each coefficients related to the common regressor, possibly with sign constraints

* betac_ci_unc: confidence intervals on each coefficients related to the common regressor without sign constraints

If projection is TRUE:

* support: confidence bound on the support function in each specified direction

- point : a list with all the information on the point estimates

* upper: the upper bounds on betanc, possibly with sign constraints

* lower: the lower bounds on betanc, possibly with sign constraints

* unconstr: bounds on betanc without sign constraints

* If common regressors, upper_agg, lower_agg, and unconstr_agg reports the same values but aggregated over the values of Xc (see the parameter theta0 in the paper)

* betac_pt: bounds on betanc, possibly with sign constraints

* betac_pt_unc: bounds on betanc without sign constraints If projection ==TRUE:

* support: point estimate of the support function in each specified direction

- epsilon : the values of the selected epsilon(q)