tau_calc: Coverage Probability Calculation for Intersection CI

In koohyun-kwon/rdadapt:

Coverage Probability Calculation for Intersection CI

Description

Calculates the (non-)coverage probabilities of individual confidence intervals that ensure the proper coverage of the intersection confidence interval.

Usage

tau_calc(
  Cvec,
  Cbar,
  Xt,
  Xc,
  mon_ind,
  sigma_t,
  sigma_c,
  alpha,
  num_sim = 10^5,
  delta_init = 1.96,
  bmat_init
)

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).
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.

Details

This solves (19) of our paper, using the asymptotic argument provided in the paper.

Value

a list of two values, del_sol, the proper value of δ to be used for individual CIs, and tau_sol, the non-coverage probability associated with the value of δ.

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]
tau_calc((1:5)/5, 1, Xt, Xc, mon_ind, sigma_t, sigma_c, 0.05)
tau_calc((1:5)/5, Inf, Xt, Xc, mon_ind, sigma_t, sigma_c, 0.05)

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