Optimal estimation for regression discontinuity design with binary outcomes

Understand

We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case.

• Our estimator achieves minimax mean squared error among linear shrinkage estimators with nonnegative weights when the regression function lies in a Lipschitz class.
• Although the original minimax problem involves an iterative noncovex optimization problem, we show that our estimator is obtained by solving a convex optimization problem.
• A key advantage of the proposed estimator is that the Lipschitz constant is its only tuning parameter.