Estimate the marginal quantile if the entire population follows a
treatment regime indexed by the given parameters.
This function supports the qestimate function.
quant_est(beta, x, y, a, prob, tau)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
a numeric value between 0 and 1. The quantile level of interest.