A First Course in Linear Model Theory

✍ Scribed by Nalini Ravishanker; Dipak K. Dey

• Publisher: CRC Press
• Year: 2020
• Tongue: English
• Leaves: 490
• Edition: 1
• Category: Library

✦ Synopsis

This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation

✦ Table of Contents

Cover Page
Table of Contents
Ch. 1 Review of Vector and Matrix Algebra
1.2 Basic definitions and properties
Exercises
Ch. 2 Properties of Special Matrices
2.1 Partitioned Matrices
2.2 Algorithms for matrix factorization
2.3 Symmetric and idempotent matrices
2.4 Nonnegative definite quadritic forms and matrices
2.5 Simultaneous diagonalization of matrices
2.6 Geometrical Perspectives
2.7 Vector and matrix differentiation
2.8 Special operations on matrices
2.9 Linear optimization
Exercises
Ch. 3 Generalized Inverses and Solutions to Linear Systems
3.1 Generalized inverses
3.2 Solutions to linear systems
Exercises
Ch. 4 The General Linear Model
4.1 Model definition and examples
4.2 The least squares approach
4.3 Estimable functions
4.4 Gauss-Markov theorem
4.5 Generalized least squares
4.6 Estimation subject to linear restrictions
Exercises
Ch. 5 Multivariate Normal and Related Distributions
5.1 Multivariate probability distributions
5.2 Multivariate normal distribution and properties
5.3 Some noncentral distributions
5.4 Distributions of quadratic forms
5.5 Alternatives to multivariate normal distribution
Exercises
Ch. 6 Sampling from the Multivariate Normal Distribution
6.1 Distribution of sample mean and covariance
6.2 Distributions related to correlation coefficients
6.3 Assessing the normality assumption
6.4 Transformations to approximate normality
Exercises
Ch. 7 Inference for the General Linear Model
7.1 Properties of least square estimates
7.2 General linear hypothesis
7.3 Confidence intervals and multiple comparisons
7.4 Restricted and reduced models
7.5 Likelihood based approaches
Exercises
Ch. 8 Multiple Regression Models
8.1 Departures from model assumptions
8.2 Model selection in regression
8.3 Orthogonal and collinear predictors
8.4 Prediction intervals and calibration
8.5 Regression diagnostics
8.6 Dummy variables in regression
8.7 Robust regression
8.8 Nonparametric regression methods
Exercises
Ch. 9 Fixed Effects Linear Models
9.1 Checking model assumptions
9.2 Inference for unbalanced ANOVA models
9.3 Analaysis of Covariance
9.4 Nonparametric procedures
Exercises
Ch. 10 Random-Effects and Mixed-Effects Models
10.1 One-factor random-effects model
10.2 Mixed-effects linear models
Exercises
Ch. 11 Special Topics
11.1 Bayesian linear models
11.2 Dynamic linear models
11.3 Longitudinal models
11.4 Generalized linear models
Exercises
A Review of Probability Distributions
Solutions to Selected Exercises
References
Author Index
Subject Index

✦ Subjects

Statistics, Linear Models, Theory of Linear Models