This involves two steps. First, you must provide the weights to be used in estimation. The second step is to request the correction to the covariance matrix. When the over or undersampling is severe, this correction often results in very large increases in the estimated standard errors.
Authors often suggest the matrix V above without weights as a robust covariance matrix.
You would need to establish the conditions to which this estimator is robust on a case by case basis, and we make no attempt here to list these. But, there is a simple trick you can use to obtain this matrix for which the choice based sampling correction is available.