迁移瓮模型的渐近性质及其应用
Immigrated urn models - asymptotic properties and applications
摘要：
瓮模型在科学和社会科学领域都得到了广泛的研究和应用。在临床研究中，在治疗分配方案中采用瓮模型已被证明对研究人员和患者都有利，前者通过提供更有效的临床试验，后者通过增加接受更好治疗的可能性。在本文中，我们提出了一个新的和一般类的移民瓮（IMU）模型，将移民机制的瓮过程。理论特性的开发和IMU模型的优点进行了讨论。一般来说，IMU模型比经典的瓮模型具有更小的变异性，在应用中产生更强大的统计推断。说明性的例子来证明IMU模型的广泛适用性。提出的IMU框架，包括许多流行的经典骨灰盒模型，不仅提供了一个统一的视角，我们理解的骨灰盒过程，但也使我们能够产生一些新的骨灰盒模型所需的属性。
英文摘要：
Urn models have been widely studied and applied in both scientific and social science disciplines. In clinical studies, the adoption of urn models in treatment allocation schemes has been proved to be beneficial to both researchers, by providing more efficient clinical trials, and patients, by increasing the likelihood of receiving the better treatment. In this paper, we propose a new and general class of immigrated urn (IMU) models that incorporates the immigration mechanism into the urn process. Theoretical properties are developed and the advantages of the IMU models are discussed. In general, the IMU models have smaller variabilities than the classical urn models, yielding more powerful statistical inferences in applications. Illustrative examples are presented to demonstrate the wide applicability of the IMU models. The proposed IMU framework, including many popular classical urn models, not only offers a unify perspective for us to comprehend the urn process, but also enables us to generate several novel urn models with desirable properties.
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