Weighted neural network and weighted least square estimators under censorship.

Abstract

We propose in this paper a hybrid approach to regression estimation under censoring combines the practical effectiveness of neural networks and the theoretical strength of the least squares method. The censoring weights are incorporated as pre-specified weighting variables in the neural network's training loss function, enabling the model to effectively account for censored observations during the learning process. Construction on this, a least squares estimator is introduced within a well-defined neural network function space to estimate the network parameters. This combination allows the method to benefit from the empirical performance of neural networks while solidifying it with strong theoretical guarantees. In particular, the paper establishes an almost sure convergence theorem for the L₂ estimation error, demonstrating the robustness of the approach. A simulation study is conducted to evaluate the performance of the estimator, and the methodology is then validated using an example on real data.