论文标题
在密度比模型下对分位数的经验可能性比测试
Empirical likelihood ratio test on quantiles under a density ratio model
论文作者
论文摘要
人口分位数是许多应用中的重要参数。在过去的十年中,对分位数及其功能开发有效的统计推断程序的热情一直很高。在本文中,我们研究了当可用的多个链接人群的样本时,我们研究了分位数的推断方法。我们认为的研究问题具有广泛的应用。例如,为了研究一个国家的经济状况的演变,经济学家根据每年收集的多个调查数据集监测年度家庭收入的分位数的变化。即使有多个样本,常规方法也会分别估计不同种群的分位数。这种方法忽略了这些人群相关并共享一些内在的潜在结构的事实。最近,许多研究人员主张使用密度比模型(DRM)来说明这种潜在结构,并根据汇总数据制定了更有效的程序。随后采用了非参数经验可能性(EL)。有趣的是,在这种情况下,没有讨论基于EL的可能性比测试(ELRT)针对人口分位数。我们探讨了ELRT用于DRM下的分位数和置信区的假设。我们表明,ELRT统计量在零假设下具有卡方限制分布。仿真实验表明,卡方分布近似有限样本分布,并导致准确的测试和置信区域。 DRM有助于提高统计效率。我们还提供了一个真实的示例,以说明所提出的方法的效率。
Population quantiles are important parameters in many applications. Enthusiasm for the development of effective statistical inference procedures for quantiles and their functions has been high for the past decade. In this article, we study inference methods for quantiles when multiple samples from linked populations are available. The research problems we consider have a wide range of applications. For example, to study the evolution of the economic status of a country, economists monitor changes in the quantiles of annual household incomes, based on multiple survey datasets collected annually. Even with multiple samples, a routine approach would estimate the quantiles of different populations separately. Such approaches ignore the fact that these populations are linked and share some intrinsic latent structure. Recently, many researchers have advocated the use of the density ratio model (DRM) to account for this latent structure and have developed more efficient procedures based on pooled data. The nonparametric empirical likelihood (EL) is subsequently employed. Interestingly, there has been no discussion in this context of the EL-based likelihood ratio test (ELRT) for population quantiles. We explore the use of the ELRT for hypotheses concerning quantiles and confidence regions under the DRM. We show that the ELRT statistic has a chi-square limiting distribution under the null hypothesis. Simulation experiments show that the chi-square distributions approximate the finite-sample distributions well and lead to accurate tests and confidence regions. The DRM helps to improve statistical efficiency. We also give a real-data example to illustrate the efficiency of the proposed method.