Given a fixed treatment regime, this doubly robust estimator estimates the marginal quantile of responses when it is followed by every unit in the target population. It took advantages of conditional quantile functions for different treatment levels when they are available.
dr_quant_est(beta, x, y, a, prob, tau, y.a.0, y.a.1, num_min = FALSE)a vector indexing the treatment regime. It indexes a linear treatment regime: $$ d(x)= I\{\beta_0 + \beta_1 x_1 + ... + \beta_k x_k > 0\}. $$
a matrix of observed covariates from the sample.
Notice that we assumed the class of treatment regimes is linear.
This is important that columns in x matches with beta.
a vector, the observed responses from a sample
a vector of 0s and 1s, the observed treatments from a sample
a vector, the propensity scores of getting treatment 1 in the samples
The quantile of interest
Estimated conditional potential outcome given that treatment = 0,
which can be calculated by the function augX.
Estimated conditional potential outcome given that treatment = 1,
which can be calculated by the function augX.
logical. If TRUE, the number of global minimizers for the
objective function is returned.
The double robustness property means that it can consistently estimate the marginal quantile when either the propensity score model is correctly specified, or the conditional quantile function is correctly specified.