compute_stat_variance: Function to compute the Variance bounds on the noncommon regressor Xnc

Description

Function to compute the Variance bounds on the noncommon regressor Xnc

Usage

compute_stat_variance(
  sample1 = NULL,
  X1_x,
  X2,
  X1_y,
  Y,
  values,
  refs0,
  dimX1,
  dimX2,
  nb_pts,
  sam0,
  lim = 1,
  weights_x = NULL,
  weights_y = NULL,
  constraint = NULL,
  c_sign = NULL,
  nc_sign = NULL,
  values_sel = NULL
)

Value

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

- 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

Arguments

sample1: if NULL compute the point estimate, if a natural number then evaluate a bootstrap or subsampling replication.
X1_x: the common regressor on the dataset (Xnc,Xc). Default is NULL.
X2: the noncommon regressor on the dataset (Xnc,Xc). No default.
X1_y: the common regressor on the dataset (Y,Xc). Default is NULL.
Y: the outcome variable. No default.
values: the different unique points of support of the common regressor Xc.
refs0: indicating the positions in the vector values corresponding to the components of betac.
dimX1: the dimension of the common regressors Xc.
dimX2: the dimension of the noncommon regressors Xnc.
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.
sam0: the directions q to compute the variance bounds on the radial function.
lim: the limit number of observations under which we do no compute the conditional variance.
weights_x: the sampling weights for the dataset (Xnc,Xc).
weights_y: the 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.
values_sel: the selected values of Xc for the conditioning. Default is NULL.