Matching a discrete distribution by Poisson matching quantiles estimation

Analyzing the data collected from different sources requires unpaired data analysis to account for the absence of correspondence between the random variable Y and the covariates X. Several attempts have been made to analyze continuous Y, but it may follow a discrete distribution, which previous methodologies have overlooked. To address these limitations, we propose Poisson matching quantiles estimation (PMQE), the first unpaired data analysis method designed to examine the discrete Y and the unpaired continuous covariates X. Using their order statistics, the PMQE method matches the linear combination of random variables βTX to log(Y). We further improve the performance of the proposed method by ℓ1 penalizing β, leading to the PMQE LASSO. An effective algorithm and simulation results are presented, along with the convergence results. We illustrate the practical application of PMQE using real data.