Abstract We investigate a simple objective for nonlinear instrumental variable (IV) regression based on kernelized conditional moment restriction known as maximum (MMR). The MMR is formulated by maximizing the interaction between residual and instruments belonging to unit ball in reproducing kernel Hilbert space. First, it allows us simplify IV an empirical risk minimization problem, where func...

In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to flexible neural network architecture, our methodology uses dimension reduction and feature selection from set instruments covariates. A central theoretical result, due Brillinger (2012) Selected Works Daving Brillinger. 589-606, shows that pro...

This paper presents instrumental variable methods for identifying partial differential equation models of distributed parameter systems in presence of output measurement noise. Two instrumental variable-based techniques are proposed to handle this continuous-time model identification problem: a basic one using input-only instruments and a more sophisticated refined instrumental variable method....