Matching a discrete distribution by Poisson matching quantiles estimation

초록

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 $\mathbf{X}$ 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 $\mathbf{X}$ X. Using their order statistics, the PMQE method matches the linear combination of random variables $\mathbf{\beta }{<}^{>}T\mathbf{X}$ beta TX to $\log (Y)$ log(Y). We further improve the performance of the proposed method by ${\ell }_1$ l1 penalizing $\mathbf{\beta }$ beta, 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.

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