Estimate the marginal mean of the response when the entire population follows a treatment regime. This function implements the inverse probability weighted estimator proposed by Baqun Zhang et. al..
This function supports the mestimate function.
mean_est(beta, x, a, y, prob)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 of 0s and 1s, the observed treatments from a sample
a vector, the observed responses from a sample
a vector, the propensity scores of getting treatment 1 in the samples
zhang2012robustquantoptr