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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. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis. The book is suitable for a course in a M.S. program in statistics, provided that the section of further results and technical notes in each of the first four chapters is skipped. If these four sections are included, the book may be used for a course in a Ph. D. program in statistics. A first course in mathematical statistics, the ability to use computers for data analysis, and familiarity with calculus and linear algebra are prerequisites. Additional statistical courses such as regression analysis and a good knowledge about matrices would be helpful. Jiming Jiang is Professor of Statistics and Director of the Statistical Laboratory at UC-Davis. He is a prominent researcher in the fields of mixed effects models and small area estimation, and co-receiver of the Chinese National Natural Science Award and American Statistical Association's Outstanding Statistical Application Award.

Mathematical statistics. --- Linear models (Statistics) --- Models, Linear (Statistics) --- Mathematical models --- Mathematical statistics --- Statistics --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Distribution (Probability theory. --- Numerical analysis. --- Genetics --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Public Health. --- Numerical Analysis. --- Genetics and Population Dynamics. --- Mathematics. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Mathematical analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities. --- Statistics . --- Public health. --- Biomathematics. --- Community health --- Health services --- Hygiene, Public --- Hygiene, Social --- Public health services --- Public hygiene --- Social hygiene --- Health --- Human services --- Biosecurity --- Health literacy --- Medicine, Preventive --- National health services --- Sanitation --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Risk

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Linear models (Statistics). --- Mathematical statistics. --- Mathematical statistics --- Linear models (Statistics) --- 519.2 --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Models, Linear (Statistics) --- Mathematical models --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Statistical methods

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This book offers a comprehensive guide to large sample techniques in statistics. More importantly, it focuses on thinking skills rather than just what formulae to use; it provides motivations, and intuition, rather than detailed proofs; it begins with very simple techniques, and connects theory and applications in entertaining 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 10 chapters contains at least one section of case study. The last five chapters are devoted to special areas of applications. The sections of case studies and chapters of applications fully demonstrate how to use methods developed from large sample theory in various, less-than-textbook situations. The book is supplemented by a large number of exercises, giving the readers plenty of opportunities to practice what they have learned. The book is mostly self-contained with the appendices providing some backgrounds for matrix algebra and mathematical statistics. The book is intended for a wide audience, ranging from senior undergraduate students to researchers with Ph.D. degrees. A first course in mathematical statistics and a course in calculus are prerequisites. Jiming Jiang is a Professor of Statistics at the University of California, Davis. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He is the author of another Springer book, Linear and Generalized Linear Mixed Models and Their Applications (2007). Jiming Jiang is a prominent researcher in the fields of mixed effects models, small area estimation and model selection. Most of his research papers have involved large sample techniques. He is currently an Associate Editor of the Annals of Statistics.

Statistical science --- Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- kansrekening --- statistisch onderzoek

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Mathematical statistics. --- Linear models (Statistics) --- Models, Linear (Statistics) --- Mathematical models --- Mathematical statistics --- Statistics --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Estadística matemàtica --- Models lineals (Estadística) --- Estadística --- Models matemàtics --- Estadística descriptiva --- Inferència estadística --- Matemàtica estadística --- Mètodes estadístics --- Anàlisi d'error (Matemàtica) --- Anàlisi de regressió --- Anàlisi de sèries temporals --- Anàlisi de variància --- Anàlisi multivariable --- Anàlisi seqüencial --- Astronomia estadística --- Correlació (Estadística) --- Dependència (Estadística) --- Estadística no paramètrica --- Estadística robusta --- Física estadística --- Mètode dels moments (Estadística) --- Models no lineals (Estadística) --- Teoria de l'estimació --- Teoria de la predicció --- Tests d'hipòtesi (Estadística) --- Biometria --- Mostreig (Estadística)

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This book offers a comprehensive guide to large sample techniques in statistics. More importantly, it focuses on thinking skills rather than just what formulae to use; it provides motivations, and intuition, rather than detailed proofs; it begins with very simple techniques, and connects theory and applications in entertaining 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 10 chapters contains at least one section of case study. The last five chapters are devoted to special areas of applications. The sections of case studies and chapters of applications fully demonstrate how to use methods developed from large sample theory in various, less-than-textbook situations. The book is supplemented by a large number of exercises, giving the readers plenty of opportunities to practice what they have learned. The book is mostly self-contained with the appendices providing some backgrounds for matrix algebra and mathematical statistics. The book is intended for a wide audience, ranging from senior undergraduate students to researchers with Ph.D. degrees. A first course in mathematical statistics and a course in calculus are prerequisites. Jiming Jiang is a Professor of Statistics at the University of California, Davis. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He is the author of another Springer book, Linear and Generalized Linear Mixed Models and Their Applications (2007). Jiming Jiang is a prominent researcher in the fields of mixed effects models, small area estimation and model selection. Most of his research papers have involved large sample techniques. He is currently an Associate Editor of the Annals of Statistics.

Statistical science --- Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- kansrekening --- statistisch onderzoek