Semiparametric Estimation of Nonseparable Models: A Minimum Distance from Independence Approach

This paper focuses on nonseparable structural models of the form Y = m(X, U, α0) with U X and in which the structural parameter α0 contains both finite dimensional (θ0) and infinite dimensional (h0) unknown components. Our proposal is to estimate α0 by a minimum distance from independence (MDI) criterion. We show that: (i) our estimator of h0 is consistent and obtain rates of convergence; (ii) the estimator of θ0 is square root n consistent and asymptotically normally distributed