Opt_C_seq: Calculates the Optimal Sequence of Lipschitz Coefficients

In koohyun-kwon/rdadapt:

Calculates the Optimal Sequence of Lipschitz Coefficients

Description

This corresponds to Procedure 3 in the paper (Ver20201104).

Usage

Opt_C_seq(
  C_l,
  C_u,
  C,
  Xt,
  Xc,
  mon_ind,
  sigma_t,
  sigma_c,
  alpha,
  n_grid = 10,
  gain_tol = 0.05,
  ratio = TRUE,
  p = Inf,
  n_sim = 10^5
)

Arguments

C_l	lower end of the adaptation range.
C_u	upper end of the adaptation range.
C	the Lipschitz coefficient for the function space we consider.
Xt	n_t by k design matrix for the treated units.
Xc	n_c by k design matrix for the control units.
mon_ind	index number for monotone variables.
sigma_t	standard deviation of the error term for the treated units (either length 1 or n_t).
sigma_c	standard deviation of the error term for the control units (either length 1 or n_c).
alpha	desired upper quantile value.
n_grid	number of grid points to evaluate the lengths.
gain_tol	stopping criterion when finding the optimal J.
ratio	the ratio measure is used if TRUE; otherwise, the difference measure is used.
p	the order of l_1-norm; the default is Inf.
n_sim	number of simulated observations to calculate the expectation of the minimum of multivariate normal random variables; the default is n_sim = 10^5.

Value

a list with components Cvec, the optimal sequence of Lipschitz coefficients, bmat, the matrix of corresponding modulus values, tau_res, the corresponding calibrated values of τ and δ, and dist_opt, the optimal distance to the orale.

Examples

n <- 500
d <- 2
X <- matrix(rnorm(n * d), nrow = n, ncol = d)
tind <- X[, 1] < 0 & X[, 2] < 0
Xt <- X[tind == 1, ,drop = FALSE]
Xc <- X[tind == 0, ,drop = FALSE]
mon_ind <- c(1, 2)
sigma <- rnorm(n)^2 + 1
sigma_t <- sigma[tind == 1]
sigma_c <- sigma[tind == 0]
Opt_C_seq(0.1, 1, 2, Xt, Xc, mon_ind, sigma_t, sigma_c, 0.05, 10, 0.05)

koohyun-kwon/rdadapt documentation built on May 8, 2022, 8:49 p.m.