Abstract
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.