Wavelet neural network modeling under censoring

Abstract

We propose a new neural network method to estimate an unknown regression function when the observed data are partially hidden due to simultaneous left- and right-censoring. The approach combines wavelet-based feature extraction with a shallow neural network, offering strong flexibility. Estimation relies on inverse probability weighting to handle censoring. We prove both standard and almost-sure convergence of the method under mild conditions on the network architecture and resolution level. The theoretical analysis draws on bias-variance decomposition, covering number arguments, and concentration inequalities.