Modern applied U-statistics [[electronic resource] /] / Jeanne Kowalski; Xin M. Tu

• Autore: Kowalski Jeanne
• Pubblicazione: Hoboken, NJ, : Wiley Pub., 2008
• Descrizione fisica: 1 online resource (402 p.)
• Disciplina: 519.52
• Soggetto topico: U-statistics; Mathematical statistics
• Soggetto genere / forma: Electronic books.
• Altri autori: TuXin M
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Modern Applied U-Statistics; Contents; Preface; 1 Preliminaries; 1.1 Introduction; 1.1.1 The Linear Regression Model; 1.1.2 The Product-Moment Correlation; 1.1.3 The Rank-Based Mann-Whitney-Wilcoxon Test; 1.2 Measurability and Measure Space; 1.2.1 Measurable Space; 1.2.2 Measure Space; 1.3 Measurable Function and Integration; 1.3.1 Measurable Functions; 1.3.2 Convergence of Sequence of Measurable Functions; 1.3.3 Integration of Measurable Functions; 1.3.4 Integration of Sequences of Measurable Functions; 1.4 Probability Space and Random Variables; 1.4.1 Probability Space ; 1.4.2 Random Variables1.4.3 Random Vectors; 1.5 Distribution Function and Expectation; 1.5.1 Distribution Function; 1.5.2 Joint Distribution of Random Vectors; 1.5.3 Expectation; 1.5.4 Conditional Expectation; 1.6 Convergence of Random Variables and Vectors; 1.6.1 Modes of Convergence; 1.6.2 Convergence of Sequence of I.I.D. Random Variables; 1.6.3 Rate of Convergence of Random Sequence; 1.6.4 Stochastic op (.) and Op (.); 1.7 Convergence of Functions of Random Vectors; 1.7.1 Convergence of Functions of Random Variables; 1.7.2 Convergence of Functions of Random Vectors; 1.8 Exercises ; 2 Models for Cross-Sectional Data2.1 Parametric Regression Models; 2.1.1 Linear Regression Model; 2.1.2 Inference for Linear Models; 2.1.3 General Linear Hypothesis; 2.1.4 Generalized Linear Models; 2.1.5 Inference for Generalized Linear Models; 2.2 Distribution-Free (Semiparametric) Models; 2.2.1 Distribution-Free Generalized Linear Models; 2.2.2 Inference for Generalized Linear Models; 2.3 Exercises; 3 Univariate U-Statistics; 3.1 U-Statistics and Associated Models; 3.1.1 One Sample U-Statistics; 3.1.2 Two-Sample and General K Sample U-Statistics ; 3.1.3 Representation of U-Statistic by Order Statistic3.1.4 Martingale Structure of U-Statistic; 3.2 Inference for U-Statistics; 3.2.1 Projection of U-statistic; 3.2.2 Asymptotic Distribution of One-Group U-Statistic; 3.2.3 Asymptotic Distribution of K-Group U-Statistic; 3.3 Exercises; 4 Models for Clustered Data; 4.1 Longitudinal versus Cross-Sectional Designs; 4.2 Parametric Models; 4.2.1 Multivariate Normal Distribution Based Models; 4.2.2 Linear Mixed-Effects Model; 4.2.3 Generalized Linear Mixed-Effects Models; 4.2.4 Maximum Likelihood Inference; 4.3 Distribution-Free Models ; 4.3.1 Distribution-Free Models for Longitudinal Data4.3.2 Inference for Distribution-Free Models; 4.4 Missing Data; 4.4.1 Inference for Parametric Models; 4.4.2 Inference for Distribution-Free Models; 4.5 GEE II for Modeling Mean and Variance; 4.6 Structural Equations Models; 4.6.1 Path Diagrams and Models; 4.6.2 Maximum Likelihood Inference; 4.6.3 GEE-Based Inference; 4.7 Exercises; 5 Multivariate U-Statistics; 5.1 Models for Cross-Sectional Study Designs; 5.1.1 One Sample Multivariate U-Statistics; 5.1.2 General K Sample Multivariate U-Statistics; 5.2 Models for Longitudinal Study Designs ; 5.2.1 Inference in the Absence of Missing Data
• Sommario/riassunto: A timely and applied approach to the newly discovered methods and applications of U-statisticsBuilt on years of collaborative research and academic experience, Modern Applied U-Statistics successfully presents a thorough introduction to the theory of U-statistics using in-depth examples and applications that address contemporary areas of study including biomedical and psychosocial research. Utilizing a ""learn by example"" approach, this book provides an accessible, yet in-depth, treatment of U-statistics, as well as addresses key concepts in asymptotic theory by integrating translatio
• Titolo autorizzato: Modern applied U-statistics
• ISBN: 1-281-20376-9; 9786611203764; 0-470-18646-1; 0-470-18645-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910144743403321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley series in probability and statistics.