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Linear Models
| Autor principal: | |
|---|---|
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Newark :
John Wiley & Sons, Incorporated,
2016.
|
| Colección: | New York Academy of Sciences Ser.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro
- Linear Models
- Contents
- Preface
- Preface to First Edition
- About the Companion Website
- Introduction and Overview
- 1 Generalized Inverse Matrices
- 1 Introduction
- a Definition and Existence of a Generalized Inverse
- b An Algorithm for Obtaining a Generalized Inverse
- c Obtaining Generalized Inverses Using the Singular Value Decomposition (SVD)
- 2 Solving Linear Equations
- a Consistent Equations
- b Obtaining Solutions
- c Properties of Solutions
- 3 The Penrose Inverse
- 4 Other Definitions
- 5 Symmetric Matrices
- a Properties of a Generalized Inverse
- B Two More Generalized Inverses of
- 6 Arbitrariness in a Generalized Inverse
- 7 Other Results
- 8 Exercises
- 2 Distributions and Quadratic Forms
- 1 Introduction
- 2 Symmetric Matrices
- 3 Positive Definiteness
- 4 Distributions
- a Multivariate Density Functions
- b Moments
- c Linear Transformations
- d Moment and Cumulative Generating Functions
- e Univariate Normal
- f Multivariate Normal
- g Central 2, F, and t
- h Non-central 2
- i Non-central F
- j The Non-central t Distribution
- 5 Distribution of Quadratic Forms
- a Cumulants
- b Distributions
- c Independence
- 6 Bilinear Forms
- 7 Exercises
- 3 Regression for the Full-Rank Model
- 1 Introduction
- a The Model
- b Observations
- c Estimation
- d The General Case of k x Variables
- e Intercept and No-Intercept Models
- 2 Deviations From Means
- 3 Some Methods of Estimation
- a Ordinary Least Squares
- b Generalized Least Squares
- c Maximum Likelihood
- d The Best Linear Unbiased Estimator (b.l.u.e.)(Gauss-Markov Theorem)
- e Least-squares Theory When The Parameters are Random Variables
- 4 Consequences of Estimation
- a Unbiasedness
- b Variances
- c Estimating E(y)
- D Residual Error Sum of Squares
- e Estimating the Residual Error Variance
- f Partitioning the Total Sum of Squares
- g Multiple Correlation
- 5 Distributional Properties
- a The Vector of Observations y is Normal
- b The Least-square Estimator ̂b is Normal
- c The Least-square Estimator ̂b and the Estimator of the Variance ̂ 2 are Independent
- d The Distribution of SSE/2 is a 2 Distribution
- e Non-central 2′ s
- f F-distributions
- g Analyses of Variance
- h Tests of Hypotheses
- i Confidence Intervals
- j More Examples
- k Pure Error
- 6 The General Linear Hypothesis
- A Testing Linear Hypothesis
- b Estimation Under the Null Hypothesis
- c Four Common Hypotheses
- d Reduced Models
- e Stochastic Constraints
- f Exact Quadratic Constraints (Ridge Regression)
- 7 Related Topics
- a The Likelihood Ratio Test
- b Type I and Type II Errors
- c The Power of a Test
- d Estimating Residuals
- 8 Summary of Regression Calculations
- 9 Exercises
- 4 Introducing Linear Models: Regression on Dummy Variables
- 1 Regression on Allocated Codes
- a Allocated Codes
- b Difficulties and Criticism
- c Grouped Variables
- d Unbalanced Data