A fiducial approach to nonparametric deconvolution problem: discrete case

TL;DR

This paper introduces a computationally efficient fiducial inference method for nonparametric discrete deconvolution, providing accurate point estimates and confidence intervals, with theoretical analysis and real data application.

Contribution

It presents a novel fiducial approach for nonparametric discrete deconvolution, including an efficient sampling algorithm and theoretical properties analysis.

Findings

Good mean squared error performance

High coverage of confidence intervals

Effective application to medical data

Abstract

Fiducial inference, as generalized by Hannig et al. (2016), is applied to nonparametric g-modeling (Efron, 2016) in the discrete case. We propose a computationally efficient algorithm to sample from the fiducial distribution, and use the generated samples to construct point estimates and confidence intervals. We study the theoretical properties of the fiducial distribution and perform extensive simulations in various scenarios. The proposed approach yields good statistical performance in terms of the mean squared error of point estimators and the coverage of confidence intervals. Furthermore, we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients (Efron, 2016).