دانلود کتاب Methods of statistical model estimation

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Front Cover
Title Page
Copyright Page
Table of Contents
Preface
Overview
Acknowledgements
1 Programming and R
1.1 Introduction
1.2 R Specifics
1.2.1 Objects
1.2.1.1 Vectors
1.2.1.2 Subsetting
1.2.2 Container Objects
1.2.2.1 Lists
1.2.2.2 Dataframes
1.2.3 Functions
1.2.3.1 Arguments
1.2.3.2 Body
1.2.3.3 Environments and Scope
1.2.4 Matrices
1.2.5 Probability Families
1.2.6 Flow Control
1.2.6.1 Conditional Execution
1.2.6.2 Loops
1.2.7 Numerical Optimization
1.3 Programming
1.3.1 Programming Style
1.3.2 Debugging
1.3.2.1 Debugging in Batch
1.3.3 Object-Oriented Programming
1.3.4 S3 Classes
1.4 Making R Packages
1.4.1 Building a Package
1.4.2 Testing
1.4.3 Installation
1.5 Further Reading
1.6 Exercises
2 Statistics and Likelihood-Based Estimation
2.1 Introduction
2.2 Statistical Models
2.3 Maximum Likelihood Estimation
2.3.1 Process
2.3.2 Estimation
2.3.2.1 Exponential Family
2.3.3 Properties
2.4 Interval Estimates
2.4.1 Wald Intervals
2.4.2 Inverting the LRT: Profile Likelihood
2.4.3 Nuisance Parameters
2.5 Simulation for Fun and Profit
2.5.1 Pseudo-Random Number Generators
2.6 Exercises
3 Ordinary Regression
3.1 Introduction
3.2 Least-Squares Regression
3.2.1 Properties
3.2.2 Matrix Representation
3.2.3 QR Decomposition
3.2.4 Example
3.3 Maximum-Likelihood Regression
3.4 Infrastructure
3.4.1 Easing Model Specification
3.4.2 Missing Data
3.4.3 Link Function
3.4.4 Initializing the Search
3.4.5 Making Failure Informative
3.4.6 Reporting Asymptotic SE and CI
3.4.7 The Regression Function
3.4.8 S3 Classes
3.4.8.1 Print
3.4.8.2 Fitted Values
3.4.8.3 Residuals
3.4.8.4 Diagnostics
3.4.8.5 Metrics of Fit
3.4.8.6 Presenting a Summary
3.4.9 Example Redux
3.4.10 Follow-up
3.5 Conclusion
3.6 Exercises
4 Generalized Linear Models
4.1 Introduction
4.2 GLM: Families and Terms
4.3 The Exponential Family
4.4 The IRLS Fitting Algorithm
4.5 Bernoulli or Binary Logistic Regression
4.5.1 IRLS
4.6 Grouped Binomial Models
4.7 Constructing a GLM Function
4.7.1 A Summary Function
4.7.2 Other Link Functions
4.8 GLM Negative Binomial Model
4.9 Offsets
4.10 Dispersion, Over- and Under-
4.11 Goodness-of-Fit and Residual Analysis
4.11.1 Goodness-of-Fit
4.11.2 Residual Analysis
4.12 Weights
4.13 Conclusion
4.14 Exercises
5 Maximum Likelihood Estimation
5.1 Introduction
5.2 MLE for GLM
5.2.1 The Log-Likelihood
5.2.2 Parameter Estimation
5.2.3 Residuals
5.2.4 Deviance
5.2.5 Initial Values
5.2.6 Printing the Object
5.2.7 GLM Function
5.2.8 Fitting for a New Family
5.3 Two-Parameter MLE
5.3.1 The Log-Likelihood
5.3.2 Parameter Estimation
5.3.3 Deviance and Deviance Residuals
5.3.4 Initial Values
5.3.5 Printing and Summarizing the Object
5.3.6 GLM Function
5.3.7 Building on the Model
5.3.8 Fitting for a New Family
5.4 Exercises
6 Panel Data
6.1 What Is a Panel Model?
6.1.1 Fixed- or Random-Effects Models
6.2 Fixed-Effects Model
6.2.1 Unconditional Fixed-Effects Models
6.2.2 Conditional Fixed-Effects Models
6.2.3 Coding a Conditional Fixed-Effects Negative Binomial
6.3 Random-Intercept Model
6.3.1 Random-Effects Models
6.3.2 Coding a Random-Intercept Gaussian Model
6.4 Handling More Advanced Models
6.5 The EM Algorithm
6.5.1 A Simple Example
6.5.2 The Random-Intercept Model
6.6 Further Reading
6.7 Exercises
7 Model Estimation Using Simulation
7.1 Simulation: Why and When?
7.2 Synthetic Statistical Models
7.2.1 Developing Synthetic Models
7.2.2 Monte Carlo Estimation
7.2.3 Reference Distributions
7.3 Bayesian Parameter Estimation
7.3.1 Gibbs Sampling
7.4 Discussion
7.5 Exercises
Bibliography
Index