Multi-Layer Neural Network: Asymptotic Properties and Variable Significance Test

A neural network is among the most popular estimators in tasks that involve regression or classification. However, its statistical properties is relatively under explored. Thus, it will be important to prove the statistical properties of neural network such as asymptotic properties and a variable significance test in the regression context. Our projects have successfully derived the asymptotic properties of ReLU networks and significance testing for smooth neural networks. Our theoretical findings are supported via simulations and a comprehensive empirical analysis from asset pricing.