a_fun: Helper Function for Worst-case Bias Calculation

In koohyun-kwon/rdadapt:

Helper Function for Worst-case Bias Calculation

Description

Calculates 0.5 * (a_{t} - a_{c}) in the worst-case formula.

Usage

a_fun(delta, Cj, Cbar, Xt, Xc, mon_ind, sigma_t, sigma_c, ht, hc)

Arguments

delta	a nonegative scalar value: it can be left unspecified if ht and hc are specified.
Cj	the smoothness parameter aiming to adapt to.
Cbar	the largest smoothness parameter.
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).
ht	the modulus value for the treated observations; it can be left unspecified if delta is specified.
hc	the modulus value for the control observations; it can be left unspecified if delta is specified.

Details

This correponds to the component in the expression (16) of our paper.

Value

a scalar value

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]
a_fun(1, 1/2, 1, Xt, Xc, mon_ind, sigma_t, sigma_c)
a_fun(1, 1/2, Inf, Xt, Xc, mon_ind, sigma_t, sigma_c)

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