Jiming Jiang – författare

Over the past decade there has been an explosion of developments in mixed e?ects models and their applications. This book concentrates on two major classes of mixed e?ects models, linear mixed models and generalized linear mixed models, with the intention of o?ering an up-to-date account of theory and methods in the analysis of these models as well as their applications in various ?elds. The ?rst two chapters are devoted to linear mixed models. We classify l- ear mixed models as Gaussian (linear) mixed models and non-Gaussian linear mixed models. There have been extensive studies in estimation in Gaussian mixed models as well as tests and con?dence intervals. On the other hand, the literature on non-Gaussian linear mixed models is much less extensive, partially because of the di?culties in inference about these models. However, non-Gaussian linear mixed models are important because, in practice, one is never certain that normality holds. This book o?ers a systematic approach to inference about non-Gaussian linear mixed models. In particular, it has included recently developed methods, such as partially observed information, iterative weighted least squares, and jackknife in the context of mixed models. Other new methods introduced in this book include goodness-of-?t tests, p- diction intervals, and mixed model selection. These are, of course, in addition to traditional topics such as maximum likelihood and restricted maximum likelihood in Gaussian mixed models.

Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.

In recent years there has been substantial and growing interest in small area estimation (SAE) that is largely driven by practical demands. Here, the term "small area" typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain.Keywords in SAE are “borrowing strength”. Because there are insufficient samples from the small areas to produce reliable direct estimates, statistical methods are sought to utilize other sources of information to do better than the direct estimates. A typical way of borrowing strength is via statistical modelling. On the other hand, there is no “free lunch”. Yes, one can do better by borrowing strength, but there is a cost. This is the main topic discussed in this text.FeaturesA comprehensive account of methods, applications, as well as some open problems related to robust SAEMethods illustrated by worked examples and case studies using real dataDiscusses some advanced topics including benchmarking, Bayesian approaches, machine learning methods, missing data, and classified mixed model predictionSupplemented with code and data via a websiteRobust Small Area Estimation: Methods, Applications, and Open Problems is primarily aimed at researchers and graduate students of statistics and data science and would also be suitable for geography and survey methodology researchers. The practical approach should help persuade practitioners, such as those in government agencies, to more readily adopt robust SAE methods. It could be used to teach a graduate-level course to students with a background in mathematical statistics.

Now in its second edition, this book covers two major classes of mixed effects models—linear mixed models and generalized linear mixed models—and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. It offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it discusses the latest developments and methods in the field, incorporating relevant updates since publication of the first edition. These include advances in high-dimensional linear mixed models in genome-wide association studies (GWAS), advances in inference about generalized linear mixed models with crossed random effects, new methods in mixed model prediction, mixed model selection, and mixed model diagnostics.This book is suitable for students, researchers, and practitioners who are interested in using mixed models for statistical data analysis with public health applications. It is best for graduate courses in statistics, or for those who have taken a first course in mathematical statistics, are familiar with using computers for data analysis, and have a foundational background in calculus and linear algebra.

Now in its second edition, this book covers two major classes of mixed effects models—linear mixed models and generalized linear mixed models—and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. It offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it discusses the latest developments and methods in the field, incorporating relevant updates since publication of the first edition. These include advances in high-dimensional linear mixed models in genome-wide association studies (GWAS), advances in inference about generalized linear mixed models with crossed random effects, new methods in mixed model prediction, mixed model selection, and mixed model diagnostics.This book is suitable for students, researchers, and practitioners who are interested in using mixed models for statistical data analysis with public health applications. It is best for graduate courses in statistics, or for those who have taken a first course in mathematical statistics, are familiar with using computers for data analysis, and have a foundational background in calculus and linear algebra.

Plant Centromere Biology is dedicated to plant centromere research. Chapters cover the structure of centromeres from several plant species including Arabidopsis thaliana, rice, maize, wheat and beet, while other sections cover several unique characteristics associated with plant centromeres, including classical and modern neocentromeres, centromere drive and centromere misdivision.  Additional chapters are dedicated to epigenetic modification and evolution of plant centromeres, and development and application of plant artificial chromosomes. Written by an international group of experts in the field, Plant Centromere Biology is a valuable handbook for all plant scientists working on plant genome research.  Beyond the bench, it can also serve as a helpful reference tool or textbook for upper level college classes on cytogenetics or genome analysis.

In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 “standard” situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson’s? -test—the asymptotic distri- 2 2 bution of Pearson’s? -test is not always? (e.g., Moore 1978).

Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.

This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways.The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science.This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..

This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways.The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science.This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..

This volume consists of 22 research papers by leading researchers in Probability and Statistics. Many of the papers are focused on themes that Professor Bhattacharya has published on research. Topics of special interest include nonparametric inference, nonparametric curve fitting, linear model theory, Bayesian nonparametrics, change point problems, time series analysis and asymptotic theory.This volume presents state-of-the-art research in statistical theory, with an emphasis on nonparametric inference, linear model theory, time series analysis and asymptotic theory. It will serve as a valuable reference to the statistics research community as well as to practitioners who utilize methodology in these areas of emphasis.

This book is about a recently developed class of strategies, known as the fence methods, which fits particularly well in non-conventional and complex model selection problems with practical considerations. The idea involves a procedure to isolate a subgroup of what are known as correct models, of which the optimal model is a member. This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from amongst those within the fence according to a criterion which can be made flexible. In particular, the criterion of optimality can incorporate consideration of practical interest, thus making model selection a real life practice.Furthermore, this book introduces a data-driven approach, called adaptive fence, which can be used in a wide range of problems involving determination of tuning parameters, or constants. Instead of relying on asymptotic theory, the fence focuses on finite-sample performance, and computation. Such features are particularly suitable to statistics in the new era.