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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 확률과 통계 > 일반
· ISBN : 9781584884811
· 쪽수 : 562쪽
목차
Linear Models: Some Historical Perspectives
The Invention of Least Squares
The Gauss?Markov Theorem
Estimability
Maximum Likelihood Estimation
Analysis of Variance (ANOVA)
Quadratic Forms and Craig’s Theorem
The Role of Matrix Algebra
The Geometric Approach
Basic Elements of Linear Algebra
Introduction
Vector Spaces
Vector Subspaces
Bases and Dimensions of Vector Spaces
Linear Transformations
Basic Concepts in Matrix Algebra
Introduction and Notation
Some Particular Types of Matrices
Basic Matrix Operations
Partitioned Matrices
Determinants
The Rank of a Matrix
The Inverse of a Matrix
Eigenvalues and Eigenvectors
Idempotent and Orthogonal Matrices
Quadratic Forms
Decomposition Theorems
Some Matrix Inequalities
Function of Matrices
Matrix Differentiation
The Multivariate Normal Distribution
History of the Normal Distribution
The Univariate Normal Distribution
The Multivariate Normal Distribution
The Moment Generating Function
Conditional Distribution
The Singular Multivariate Normal Distribution
Related Distributions
Examples and Additional Results
Quadratic Forms in Normal Variables
The Moment Generating Function
Distribution of Quadratic Forms
Independence of Quadratic Forms
Independence of Linear and Quadratic Forms
Independence and Chi-Squaredness of Several Quadratic Forms
Computing the Distribution of Quadratic Forms
Appendix
Full-Rank Linear Models
Least-Squares Estimation
Properties of Ordinary Least-Squares Estimation
Generalized Least-Squares Estimation
Least-Squares Estimation under Linear Restrictions on β
Maximum Likelihood Estimation
Inference Concerning β
Examples and Applications
Less-Than-Full-Rank Linear Models
Parameter Estimation
Some Distributional Properties
Reparameterized Model
Estimable Linear Functions
Simultaneous Confidence Intervals on Estimable Linear Functions
Simultaneous Confidence Intervals on All Contrasts among the Means with Heterogeneous Group Variances
Further Results Concerning Contrasts and Estimable Linear Functions
Balanced Linear Models
Notation and Definitions
The General Balanced Linear Model
Properties of Balanced Models
Balanced Mixed Models
Complete and Sufficient Statistics
ANOVA Estimation of Variance Components
Confidence Intervals on Continuous Functions of the Variance Components
Confidence Intervals on Ratios of Variance Components
The Adequacy of Satterthwaite’s Approximation
Satterthwaite’s Approximation
Adequacy of Satterthwaite’s Approximation
Measuring the Closeness of Satterthwaite’s Approximation
Examples
Appendix
Unbalanced Fixed-Effects Models
The R-Notation
Two-Way Models without Interaction
Two-Way Models with Interaction
Higher-Order Models
A Numerical Example
The Method of Unweighted Means
Unbalanced Random and Mixed Models
Estimation of Variance Components
Estimation of Estimable Linear Functions
Inference Concerning the Random One-Way Model
Inference Concerning the Random Two-Way Model
Exact Tests for Random Higher-Order Models
Inference Concerning the Mixed Two-Way Model
Inference Concerning the Random Two-Fold Nested Model
Inference Concerning the Mixed Two-Fold Nested Model
Inference Concerning the General Mixed Linear Model
Appendix
Additional Topics in Linear Models
Heteroscedastic Linear Models
The Random One-Way Model with Heterogeneous Error Variances
A Mixed Two-Fold Nested Model with Heteroscedastic Random Effects
Response Surface Models
Response Surface Models with Random Block Effects
Linear Multiresponse Models
Generalized Linear Models
Introduction
The Exponential Family
Estimation of Parameters
Goodness of Fit
Hypothesis Testing
Confidence Intervals
Gamma-Distributed Response
Bibliography
Index
Exercises appear at the end of each chapter, except for Chapter 1.