A sliced Wasserstein and diffusion approach to random coefficient models

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency. We demonstrate that the proposed method is consistent in approximating the true distribution. Moreover, our formulation naturally leads to a diffusion process-based algorithm and is closely connected to treatment effect distribution estimation -- both of which are of independent interest and hold promise for broader applications.