Asymptotic Theory of Expectile Neural Networks

TL;DR

This paper introduces expectile neural networks, a new method that uses sieve constraints to ensure consistency and normality in large-parameter settings, expanding neural network applications in statistical genetics.

Contribution

It proposes a novel expectile neural network approach with theoretical guarantees under nonparametric regression, addressing issues with standard maximum likelihood methods.

Findings

Proves consistency and normality of the expectile neural network estimator.

Demonstrates the method's applicability in high-dimensional parameter spaces.

Provides theoretical foundation for neural networks in statistical genetics.

Abstract

Neural networks are becoming an increasingly important tool in applications. However, neural networks are not widely used in statistical genetics. In this paper, we propose a new neural networks method called expectile neural networks. When the size of parameter is too large, the standard maximum likelihood procedures may not work. We use sieve method to constrain parameter space. And we prove its consistency and normality under nonparametric regression framework.