Methods of multivariate analysis / / Alvin C. Rencher

• Autore: Rencher Alvin C. <1934->
• Pubblicazione: New York, : J. Wiley, 2002
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (739 p.)
• Disciplina: 519.535
• Soggetto topico: Multivariate analysis; Mathematical statistics
• Note generali: "A Wiley-Interscience publication."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Methods of Multivariate Analysis Second Edition; Contents; Preface; Acknowledgments; 1. Introduction; 1.1 Why Multivariate Analysis?; 1.2 Prerequisites; 1.3 Objectives; 1.4 Basic Types of Data and Analysis; 2. Matrix Algebra; 2.1 Introduction; 2.2 Notation and Basic Definitions; 2.2.1 Matrices, Vectors, and Scalars; 2.2.2 Equality of Vectors and Matrices; 2.2.3 Transpose and Symmetric Matrices; 2.2.4 Special Matrices; 2.3 Operations; 2.3.1 Summation and Product Notation; 2.3.2 Addition of Matrices and Vectors; 2.3.3 Multiplication of Matrices and Vectors; 2.4 Partitioned Matrices; 2.5 Rank ; 2.6 Inverse2.7 Positive Definite Matrices; 2.8 Determinants; 2.9 Trace; 2.10 Orthogonal Vectors and Matrices; 2.11 Eigenvalues and Eigenvectors; 2.11.1 Definition; 2.11.2 I + A and I - A; 2.11.3 tr(A) and |A|; 2.11.4 Positive Definite and Semidefinite Matrices; 2.11.5 The Product AB; 2.11.6 Symmetric Matrix; 2.11.7 Spectral Decomposition; 2.11.8 Square Root Matrix; 2.11.9 Square Matrices and Inverse Matrices; 2.11.10 Singular Value Decomposition; 3. Characterizing and Displaying Multivariate Data; 3.1 Mean and Variance of a Univariate Random Variable ; 3.2 Covariance and Correlation of Bivariate Random Variables3.2.1 Covariance; 3.2.2 Correlation; 3.3 Scatter Plots of Bivariate Samples; 3.4 Graphical Displays for Multivariate Samples; 3.5 Mean Vectors; 3.6 Covariance Matrices; 3.7 Correlation Matrices; 3.8 Mean Vectors and Covariance Matrices for Subsets of Variables; 3.8.1 Two Subsets; 3.8.2 Three or More Subsets; 3.9 Linear Combinations of Variables; 3.9.1 Sample Properties; 3.9.2 Population Properties; 3.10 Measures of Overall Variability; 3.11 Estimation of Missing Values; 3.12 Distance between Vectors ; 4. The Multivariate Normal Distribution4.1 Multivariate Normal Density Function; 4.1.1 Univariate Normal Density; 4.1.2 Multivariate Normal Density; 4.1.3 Generalized Population Variance; 4.1.4 Diversity of Applications of the Multivariate Normal; 4.2 Properties of Multivariate Normal Random Variables; 4.3 Estimation in the Multivariate Normal; 4.3.1 Maximum Likelihood Estimation; 4.3.2 Distribution of y and S; 4.4 Assessing Multivariate Normality; 4.4.1 Investigating Univariate Normality; 4.4.2 Investigating Multivariate Normality; 4.5 Outliers; 4.5.1 Outliers in Univariate Samples ; 4.5.2 Outliers in Multivariate Samples5. Tests on One or Two Mean Vectors; 5.1 Multivariate versus Univariate Tests; 5.2 Tests on m with S Known; 5.2.1 Review of Univariate Test for H(0): m = m(0) with s Known; 5.2.2 Multivariate Test for H(0): m = m(0) with S Known; 5.3 Tests on m When S Is Unknown; 5.3.1 Review of Univariate t-Test for H(0): m = m(0) with s Unknown; 5.3.2 Hotelling's T(2)-Test for H(0): m = m(0) with S Unknown; 5.4 Comparing Two Mean Vectors; 5.4.1 Review of Univariate Two-Sample t-Test; 5.4.2 Multivariate Two-Sample T(2)-Test; 5.4.3 Likelihood Ratio Tests ; 5.5 Tests on Individual Variables Conditional on Rejection of H(0) by the T(2)-Test
• Sommario/riassunto: Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Methods of Multivariate Analysis was among those chosen. When measuring several variables on a complex experimental unit, it is often necessary to analyze the variables simultaneously, rather than isolate them and consider them individually. Multivariate analysis enables researchers to explore the joint performance of such variables and to determine the effect of each variable in the presence of the others. The Second Edition of Alvin Rencher's Methods of Multivariate An
• Titolo autorizzato: Methods of multivariate analysis
• ISBN: 1-280-36701-6; 9786610367016; 0-470-35680-4; 0-471-46172-5; 0-471-27135-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910877249103321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley series in probability and mathematical statistics.