Archer Gong Zhang, Jiahua Chen
arXiv 16 Sep 2023 · Statistics — Methodology
arXiv:2309.09103 · PDF · DOI · OpenAlex · Extracted main text
In many statistical and econometric applications, we gather individual samples from various interconnected populations that undeniably exhibit common latent structures. Utilizing a model that incorporates these latent structures for such data enhances the efficiency of inferences. Recently, many researchers have been adopting the semiparametric density ratio model (DRM) to address the presence of latent structures. The DRM enables estimation of each population distribution using pooled data, resulting in statistically more efficient estimations in contrast to nonparametric methods that analyze each sample in isolation. In this article, we investigate the limit of the efficiency improvement attainable through the DRM. We focus on situations where one population's sample size significantly exceeds those of the other populations. In such scenarios, we demonstrate that the DRM-based inferences for populations with smaller sample sizes achieve the highest attainable asymptotic efficiency as if a parametric model is assumed. The estimands we consider include the model parameters, distribution functions, and quantiles. We use simulation experiments to support the theoretical findings with a specific focus on quantile estimation. Additionally, we provide an analysis of real revenue data from U.S. collegiate sports to illustrate the efficacy of our contribution.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | J. Chen and Y. Liu (2013) Quantile and quantile-function estimations under density ratio model | 0.894 | 7 | 5 | 71% |
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| 3 | B. Zhang (2000) Quantile estimation under a two-sample semi-parametric model | 0.843 | 3 | 3 | 100% |
| 4 | S. Cai, J. Chen, and J. V. Zidek (2017) Hypothesis testing in the presence of multiple samples under density ratio models | 0.644 | 2 | 2 | 100% |
| 5 | J. Qin (1993) Empirical likelihood in biased sample problems | 0.644 | 2 | 2 | 100% |
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| 10 | O. E. Barndorff-Nielsen (1988) Parametric Statistical Models and Likelihood, volume 50 of Lecture Notes in Statistics | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 42 scored citations.