Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimal

ArXi:2411.19653v2 Announce Type: replace-cross We study the kernel instrumental variable (KIV) algorithm, a kernel-based two-stage least-squares method for nonparametric instrumental variable regression. We provide a convergence analysis covering both identified and non-identified regimes: when the structural function is not identified, we show that the KIV estimator converges to the minimum-norm IV solution in the reproducing kernel Hilbert space associated with the kernel. Crucially, we establish convergence in the strong $L_2$ norm, rather than only in a pseudo-norm.