# cdensity: Doubly robust series estimation of counterfactual densities In ehkennedy/npcausal: Nonparametric causal inference methods

## Description

`cdensity` is used to estimate counterfactual densities, i.e., the density of the potential outcome in a population if everyone received given treatment levels, using doubly robust estimates of L2 projections of the density onto a linear basis expansion. Nuisance functions are estimated with random forests. The L2 distance between the density of the counterfactuals is also estimated as a density-based treatment effect.

## Usage

 ```1 2 3``` ```cdensity(y, a, x, kmax=5, l2 = TRUE, gridlen=20, nsplits=2, progress_updates = TRUE, makeplot=TRUE, kforplot=5, ylim=NULL) ```

## Arguments

 `y` outcome of interest. `a` binary treatment (more than 2 levels are allowed, but only densities under A=1 and A=0 will be estimated). `x` covariate matrix. `kmax` Integer indicating maximum dimension of (cosine) basis expansion that should be used in series estimator. `l2` A `logical` value indicating whether an estimate of the L2 distance between counterfactual densities (under A=1 vs A=0) should be returned. `gridlen` Integer number indicating length of grid for which the plug-in estimator of the marginal density is computed. `nsplits` Integer number of sample splits for nuisance estimation. If `nsplits = 1`, sample splitting is not used, and nuisance functions are estimated n full sample (in which case validity of standard errors and confidence intervals requires empirical process conditions). Otherwise must have `nsplits > 1`. `progress_updates` A `logical` value indicating whether to print a progress statement as various stages of computation reach completion. The default is `TRUE`, printing a progress bar to inform the user. `makeplot` A `logical` value indicating whether to print a plot. `kforplot` A vector of two integers indicating which k values to plot results for, with first argument for A=1 and second for A=0. `ylim` Range of y values at which density should be plotted.

## Value

A list containing the following components:

 `res` estimates/SEs/CIs/p-values for population means and relevant contrasts. `nuis` subject-specific estimates of nuisance functions (i.e., propensity score and outcome regression) `ifvals` matrix of estimated influence function values.

## References

Kennedy EH, Wasserman LA, Balakrishnan S. Semiparametric counterfactual density estimation. arxiv:TBA

## Examples

 ```1 2 3 4``` ```n <- 100; x <- matrix(rnorm(n*5),nrow=n) a <- sample(3,n,replace=TRUE)-2; y <- rnorm(n) cdens.res <- cdensity(y,a,x) ```

ehkennedy/npcausal documentation built on Feb. 26, 2021, 2:43 a.m.