CI_adpt_L: Lower Adaptive Confidence Interval

In koohyun-kwon/rdadapt:

Lower Adaptive Confidence Interval

Description

Calculates the value of the lower end of the adaptive confidence interval.

Usage

CI_adpt_L(
  Cvec,
  Cbar,
  Xt,
  Xc,
  mon_ind,
  sigma_t,
  sigma_c,
  Yt,
  Yc,
  alpha,
  num_sim = 10^5,
  delta_init = 1.96,
  bmat_init,
  bmat,
  tau_res
)

Arguments

Cvec	a sequence of smoothness parameters
Cbar	the Lipschitz coefficient for the largest 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).
Yt	outcome value for the treated group observations.
Yc	outcome value for the control group observations.
alpha	desired upper quantile value.
num_sim	number of simulations used to calculate the quantile; the default is 10^5.
delta_init	the value of δ to be used in simulating the quantile; theoretically, its value does not matter asymptotically. Its default value is 1.96.
bmat_init	the matrix of modulus values corresponding to delta_init and Cvec; it can be left unspecified.
bmat	the matrix of modulus values corresponding to the optimal δ and Cvec; it can be left unspecified.
tau_res	outcome value from the function tau_res; it can be left unspecified.

Value

a list components CI which gives the value of the lower end of the confidence interval, CI_vec which gives the values of all CIs used to compute the adaptive CI, and tau_sol which gives the value of non-coverage probability used to compute individual CIs.

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]
Yt = 1 + rnorm(length(sigma_t), mean = 0, sd = sigma_t)
Yc = rnorm(length(sigma_c), mean = 0, sd = sigma_c)
CI_adpt_L((1:5)/5, 1, Xt, Xc, mon_ind, sigma_t, sigma_c, Yt, Yc, 0.05)
CI_adpt_L((1:5)/5, Inf, Xt, Xc, mon_ind, sigma_t, sigma_c, Yt, Yc, 0.05)

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