The HilbertOneStep package implements one-step estimators of Hilbert-valued parameters, as evaluated in the simulation study from:
"One-Step Estimation of Differentiable Hilbert-Valued Parameters" by A. Luedtke and I. Chung [link]
To install the package using devtools, run the following commands:
library(devtools)
devtools::install_github("alexluedtke12/HilbertOneStep")This package includes four key functions. The first two estimate the counterfactual density under treatment A=1, assuming there are no unmeasured confounders and the positivity assumption holds. The first function implements a regularized one-step estimator that is consistent within a nonparametric model under conditions. See Luedtke and Chung (2023) for rate of convergence guarantees for this estimator.
# load the package
library(HilbertOneStep)
# sample size
n = 500
# simulate data
dat = sim_data(n,setting='zeroBothSides')
W = dat$W
A = dat$A
Y = dat$Y
cv_out = cv_density(W,A,Y,ngrid=500,num_fold_final=2)
cv_out$which_best
ygrid = seq(0.0025,0.9975,by=0.0025)
plot(ygrid,cv_out$best_fun(ygrid),xlab='y',ylab='Counterfactual Density Estimate',type='l')If it is known that the counterfactual density is bandlimited, a non-regularized one-step estimator of the counterfactual density is available. This estimator achieves a parametric rate of convergence, with mean integrated squared error converging to zero at a rate of 1/n.
# sample size
n = 500
# simulate data
dat = sim_data_bandlimited(n)
W = dat$W
A = dat$A
Y = dat$Y
bl_out = bandlimited_density(W,A,Y,ngrid=500,num_fold=2,num_boot=2000,alpha=seq(0.01,0.99,by=0.01),b=2)
ygrid = seq(-15,15,by=0.01)
plot(ygrid,bl_out$onestep_fun(ygrid),xlab='y',ylab='Counterfactual Density Estimate',type='l')The package also implements tests to determine whether the counterfactual distributions of the outcome under interventions that set A=1 and A=0 are the same.
# sample size
n = 250
# simulate data from alternative
dat = sim_data(n,setting='nonzeroBothSides',cos_parameter=1)
W = dat$W
A = dat$A
Y = dat$Y
# a test based on a weighted and standardized L2 statistic that contrasts the counterfactual density functions under A=1 and A=0
density_test(W,A,Y,num_fold=2)
# a test based on the maximum mean discrepancy between the counterfactual distributions under A=1 and A=0
mmd_test(W,A,Y,num_fold=2)
# simulate data from null
dat = sim_data(n,setting='nonzeroBothSides',cos_parameter=0)
W = dat$W
A = dat$A
Y = dat$Y
# a test based on a weighted and standardized L2 statistic that contrasts the counterfactual density functions under A=1 and A=0
density_test(W,A,Y,num_fold=2)
# a test based on the maximum mean discrepancy between the counterfactual distributions under A=1 and A=0
mmd_test(W,A,Y,num_fold=2)