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

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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.