HOIFCar (version 1.1.1)

get_oracle_bias_var_adj_2_3: Estimate the oracle bias, the exact variance and approximated variance of the debiased estimator and the bias-free estimator motivated by HOIF (Zhao et al.(2024)).

Description

Estimate the oracle bias, the exact variance and approximated variance of the debiased estimator and the bias-free estimator motivated by HOIF (Zhao et al.(2024)).

Usage

get_oracle_bias_var_adj_2_3(X, Y1, n1 = NULL)

Value

A list of oracle bias and variance of the adjusted estimator motivated by HOIF and the bias-free estimator.

bias_adj2

The oracle bias of the estimator tau_adj2.

variance_exact_adj2

The oracle exact variance of the estimator tau_adj2.

variance_approx_adj2

The oracle approximated variance of the estimator tau_adj2 which omits the term of order o(1/n).

variance_exact_adj3

The oracle exact variance of the bias-free estimator tau_adj3.

variance_unadj

The oracle variance of the unadjusted estimator.

Arguments

X

The n by p covariates matrix.

Y1

Vector of n dimensional potential response Y(1).

n1

The number of subjects in the treatment group.

References

Zhao, S., Wang, X., Liu, L., & Zhang, X. (2024). Covariate adjustment in randomized experiments motivated by higher-order influence functions. arXiv preprint. https://arxiv.org/abs/2411.08491

Examples

# Linear setting
set.seed(100)
n <- 500
p <- 50
beta <- rt(p,3)

X <- mvtnorm::rmvt(n, sigma = diag(1, p), df = 3)
Y1 <- as.numeric(X %*% beta)
pi1 <- 0.50
n1 <- ceiling(n*pi1)

result_adj_db <- get_oracle_bias_var_adj_db(X = X,Y1=Y1,n1=n1)
result_adj2c <- get_oracle_bias_var_adj2c(X = X,Y1=Y1,n1=n1)
result_adj2_3 <- get_oracle_bias_var_adj_2_3(X = X,Y1=Y1,n1=n1)
unlist(result_adj_db)
unlist(result_adj2c)
unlist(result_adj2_3)



# Nonlinear setting
n <- 500;
alpha <- 0.2;
set.seed(1000)
p <- ceiling(n*alpha)
Sigma_true <- matrix(0,nrow=p,ncol=p)
for(i in 1:p){
  for(j in 1:p){
    Sigma_true[i,j] <- 0.1**(abs(i-j))
  }
}

X <- mvtnorm::rmvt(n, sigma = Sigma_true, df = 3)
beta <- rt(p,3)
or_baseline <- sign(X %*% beta) * abs(X %*% beta)^(1/2) + sin(X %*% beta)
epsilon1 <- epsilon0 <- rt(n,3)
Y1 <- 1 + as.numeric(or_baseline) + epsilon1


pi1 <- 0.50
n1 <- ceiling(n*pi1)

result_adj_db <- get_oracle_bias_var_adj_db(X = X,Y1=Y1,n1=n1) # from LYW paper
result_adj2c <- get_oracle_bias_var_adj2c(X = X,Y1=Y1,n1=n1)
result_adj2_3 <- get_oracle_bias_var_adj_2_3(X = X,Y1=Y1,n1=n1)
unlist(result_adj_db)
unlist(result_adj2c)
unlist(result_adj2_3)