New Developments on Confidence Distributions (CDs) and Statistical Inference: Theory, Methodology and Applications

基本的统计方法，如点估计，置信区间和p值，是分析信息和数据的常用推理工具。置信分布（CD），也被称为“分布估计量”，包含了丰富的信息，是构建所有类型的频率论者统计推断的有用工具。最近的一些发展突出了CD概念作为一种有效的推理工具的潜力。作为一个新兴的研究领域，有许多重要的主题和有趣的问题尚未得到回答。建议的研究解决了几个问题，CD推理的理论框架，并提供了有用的推理工具的一些问题，其中具有良好性能的频率论方法以前不可用或难以获得。具体而言，它建议：1）利用CD随机变量的概念，开发一个通用的新框架，并研究与开发相关的理论问题。这种方法可以被认为是一个扩展的良好的研究和广泛应用的引导方法，虽然这是一个更广泛的。2)开发一种新的有效的荟萃分析方法，以联合收割机CD的多变量参数。这一发展不仅解决了传统元分析中存在的一些问题，而且在渐近理论的支持下，扩展形成了一种“分裂与征服”的策略，在大规模、大维度数据挖掘中具有潜在的应用价值。3)发展和推广CD推断的理论框架，包括：发展精确的CD概念和离散分布小样本的推断过程，并引入无限维参数（过程）的CD概率测度，并探索其在生存分析和生长曲线模型中的应用。先进的数据采集和存储技术使数据和信息的收集变得容易。对处理和分析这些信息和数据的有效统计推断方法的需求从未如此之大。该提案解决了统计推断中的几个基本理论问题以及来自各个学科的一系列重要实际问题。统计理论的进步和方法的发展是拟议活动的关键方面。这些进步不仅解决了本提案中提出的一系列具体问题，而且为频率论、基准论和贝叶斯方法带来了新的视角。这一建议的进展将进一步推进统计推断理论和统计方法的发展。它还可以促进各种领域的许多应用，包括医学研究，农业，工业，决策等。拟议的研究活动也是吸引学生参与和培训的理想选择。通过这些项目，学生可以获得与真实的生活问题的实践经验。这种培训对于他们今后成为有效的统计人员至关重要。

Basic statistical methods, such as point estimators, confidence intervals and p-values, are common inferential tools for analyzing information and data. Confidence distribution (CD), also known as a "distribution estimator," contains a wealth of information and is a useful device for constructing all types of frequentists' statistical inferences. Some recent developments have highlighted promising potentials of the CD concept as an effective inferential tool. As an emerging new field of research, there are many important topics and interesting questions yet to be answered. The proposed research addresses several issues related to the theoretical framework of CD inference, and provides useful inference tools for a number of problems where frequentist methods with good properties were previously unavailable or difficult to obtain. Specifically, it proposes to: 1) Develop a general and new framework for resampling, utilizing a concept called CD random variables, and investigate theoretical issues related to the development. This resampling approach can be considered as an extension of the well-studied and widely-applied bootstrap methods, albeit one which is much broader. 2) Develop a new and effective meta-analysis approach to combine CDs of multivariate parameters. This development not only provides solutions to several existing problems in conventional meta-analysis, but also is extended to form a "split and conquer" strategy, with supporting asymptotic theory, which has potential applications in mining data of huge size and large dimensions. 3) Develop and generalize the theoretical framework for CD inference including: developing an exact CD concept and inference procedure for small samples from discrete distributions, and introducing a CD probability measure for infinite dimensional parameters (processes) and exploring its applications in survival analysis and growth curve models. Advanced data acquisition and storage technologies have made it easy for gathering of data and information. The demand for effective statistical inference methods for processing and analyzing those information and data has never been greater. The proposal addresses several fundamental theoretical issues in statistical inference as well as a set of important practical problems arising from various disciplines. Advances in statistical theory and methodological developments are key aspects of the proposed activities. These advances not only solve the specific set of problems set forth in this proposal, but also bring about new perspectives to frequentist, fiducial and Bayesian approaches. Progress from this proposal should further advance theory of statistical inference and development of statistical methodology. It can also facilitate many applications in a variety of fields, including medical research, agriculture, industry, decision making, among others. The proposed research activities are also ideal for engaging student participation and training. Through these projects, students can acquire hands-on experience with real life problems. Such training is essential for them to become effective statisticians in the future.