Function to compute the DGM bounds on the noncommon regressor Xnc
compute_radial(
sample1 = NULL,
Xc_x,
Xnc,
Xc_y,
Y,
values,
dimXc,
dimXnc,
nb_pts,
sam0,
eps_default0,
grid = NULL,
lim = 10,
weights_x = NULL,
weights_y = NULL,
constraint = NULL,
c_sign = NULL,
nc_sign = NULL,
refs0 = NULL,
type = "both",
meth = "adapt",
version = "first",
R2bound = NULL,
values_sel = NULL,
ties = FALSE,
modeNA = FALSE
)a list containing:
- upper: the upper bound in the specified directions, possibly with sign constraints
- lower: the lower bound in the specified directions, possibly with sign constraints
- unconstr: the bounds without sign constraints in the specified directions
* 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)
- Ykmean: the means of Y|Xc for the considered sample
- Xkmean: the means of Xnc|Xc for the considered sample
- DYk: the difference of means of Y|Xc =k - Y|Xc =0 for the considered sample
- DXk: the difference of means of Xnc|Xc =k - Xnc|Xc =0 for the considered sample
- tests: the pvalues of the tests H0 : DXk =0
- ratio_ref: the ratio R in the radial function computed for the initial sample
if NULL compute the point estimate, if a natural number then evaluate a bootstrap or subsampling replication.
the common regressor on the dataset (Xnc,Xc). Default is NULL.
the noncommon regressor on the dataset (Xnc,Xc). No default.
the common regressor on the dataset (Y,Xc). Default is NULL.
the outcome variable. No default.
the different unique points of support of the common regressor Xc.
the dimension of the common regressors Xc.
the dimension of the noncommon regressors Xnc.
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 directions q to compute the variance bounds on the radial function.
the matrix containing the directions q and the selected epsilon(q).
the number of points for the grid search on epsilon. Default is 30. If NULL, then epsilon is taken fixed equal to kp.
the limit number of observations under which we do no compute the conditional variance.
the sampling weights for the dataset (Xnc,Xc).
the sampling weights for the dataset (Y,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.
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 contraints.
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 contraints.
indicating the positions in the vector values corresponding to the components of betac.
equal to "both", "up", or "low".
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".
version of the computation of the ratio, "first" indicates no weights, no ties, same sizes of the two datasets; "second" otherwise. Default is "second".
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.
indicates if NA introduced if the interval is empty. Default is FALSE.