This function compute the DGM bounds for all the different coefficients.
DGM_bounds(
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 = "second",
version_sel = "second",
alpha = 0.05,
projections = FALSE,
R2bound = NULL,
values_sel = NULL,
ties = FALSE,
mult = NULL,
seed = 2131
)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)
dataset containing (Y,Xc) where Y is the outcome, Xc are potential common regressors.
dataset containing (Xnc,Xc) where Xnc are the non commonly observed regressors, Xc are potential common regressors.
the different unique points of support of the common regressor Xc.
the directions q to compute the radial function.
indicating the positions in the vector values corresponding to the components of betac.
label of the outcome variable Y.
label of the non commonly observed regressors Xnc.
label of the commonly observed regressors Xc.
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.#' @param nc_sign if 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.
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.
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.
number of cores for the parallel computation. Default is 1.
If grid =NULL, then epsilon is taken equal to eps_default.
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.
the number of bootstrap/subsampling replications. Default is 1000.
the number of points for the grid search on epsilon. Default is 30. If NULL, then epsilon is taken fixed equal to kp.
the sampling weights for the dataset (Xnc,Xc). Default is NULL.
the sampling weights for the dataset (Y,Xc). Default is NULL.
if TRUE indicates that the parallel computing has been launched outside of the function. Default is FALSE.
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".
indicates if NA introduced if the interval is empty. Default is FALSE.
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 of the selection of the epsilon, "first" indicates no weights, no ties, same sizes of the two datasets; "second" otherwise. Default is "second".
for the level of the confidence region. Default is 0.05.
if FALSE compute the identified set along some directions or the confidence regions. Default is FALSE
the lower bound on the R2 of the long regression if any. Default is NULL.
the selected values of Xc for the conditioning. Default is NULL.
Boolean indicating if there are ties in the dataset. Default is FALSE.
a list of multipliers of our selected epsilon to look at the robustness of the point estimates with respect to it. Default is NULL
set a seed to fix the subsampling replications
n=200
Xnc_x = rnorm(n,0,1.5)
Xnc_y = rnorm(n,0,1.5)
epsilon = rnorm(n,0,1)
## true value
beta0 =1
Y = Xnc_y*beta0 + epsilon
out_var = "Y"
nc_var = "Xnc"
# create the datasets
Ldata<- as.data.frame(Y)
colnames(Ldata) <- c(out_var)
Rdata <- as.data.frame(Xnc_x)
colnames(Rdata) <- c(nc_var)
values = NULL
s= NULL
refs0 = NULL
sam0 <- rbind(-1,1)
eps0 = 0
############# Estimation #############
output <- DGM_bounds(Ldata,Rdata,values,sam0,refs0,out_var,nc_var)
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