Variance_bounds: Function to compute the variance bounds for Xnc

Description

Function to compute the variance bounds for Xnc

Usage

Variance_bounds(
  Ldata,
  Rdata,
  out_var,
  c_var,
  nc_var,
  constraint = NULL,
  c_sign = NULL,
  nc_sign = NULL,
  projections = TRUE,
  values,
  sam0,
  refs0,
  nb_pts,
  eps_default,
  nbCores,
  Bsamp = 2000,
  weights_x = NULL,
  weights_y = NULL,
  outside = FALSE,
  alpha = 0.05,
  values_sel = NULL,
  seed = 21
)

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 betanc at level alpha, possibly with sign constraints

- lower: lower bound upper bound of the confidence interval on betanc, possibly with sign constraints

- unconstr: confidence interval on betanc, without sign constraints

- 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

- 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

-betac_pt: bounds on betanc, possibly with sign constraints

-betac_pt_unc: bounds on betanc without sign constraints

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
out_var: label of the outcome variable Y.
c_var: label of the commonly observed regressors Xc.
nc_var: label of the non commonly observed regressors Xnc.
constraint: vector of the size of X_c indicating the type of constraint if any on f(X_c) : "monotone", "convex", "sign", or "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.
projections: if FALSE compute the identified set along some directions or the confidence regions. Default is FALSE.
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.
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.
eps_default: If data_k =NULL, then epsilon is taken equal to eps_default.
nbCores: number of cores for the parallel computation. Default is 1.
Bsamp: the number of bootstrap/subsampling replications. Default is 1000.
weights_x: the sampling weights for the dataset (Xnc,Xc).
weights_y: the sampling weights for the dataset (Y,Xc).
outside: if TRUE indicates that the parallel computing has been launched outside of the function. Default is FALSE.
alpha: for the level of the confidence region. Default is 0.05.
values_sel: the selected values of Xc for the conditioning. Default is NULL.
seed: set a seed to fix the subsampling replications