A0710
Title: Estimation based on martingale difference divergence
Authors: Kunyang Song - The University of Hong Kong (Hong Kong) [presenting]
Abstract: Finding valid instrumental variables (IVs) is important but hard in the linear regression model. However, the classical estimation method, such as the 2-stage least square estimator, is not applicable when the linear regression model is under-identified without enough valid IVs. Based on the martingale difference divergence (MDD), a new estimator is proposed for the general nonlinear regression model, and this estimator is applicable even when the regression model is under-identified. Under certain regular conditions, the consistency and asymptotic normality of this MDD-based estimator is established. As an extension, a new MDD-based loss function with an additional L$_1$ penalty is proposed to select non-zero parameters in several kinds of deep neural networks and further enables the causal discovery. Simulations are also given to illustrate the importance of the proposed estimators.
