  Neural networks (NN) play a central role in modern Artificial intelligence
(AI) technology and has been successfully used in areas such as natural
language processing and image recognition. While majority of NN applications
focus on prediction and classification, there are increasing interests in
studying statistical inference of neural networks. The study of NN statistical
inference can enhance our understanding of NN statistical proprieties.
Moreover, it can facilitate the NN-based hypothesis testing that can be applied
to hypothesis-driven clinical and biomedical research. In this paper, we
propose a sieve quasi-likelihood ratio test based on NN with one hidden layer
for testing complex associations. The test statistic has asymptotic chi-squared
distribution, and therefore it is computationally efficient and easy for
implementation in real data analysis. The validity of the asymptotic
distribution is investigated via simulations. Finally, we demonstrate the use
of the proposed test by performing a genetic association analysis of the
sequencing data from Alzheimer's Disease Neuroimaging Initiative (ADNI).
