Book:George C. Casella/Statistical Inference/Second Edition

Subject Matter

 * Statistics

Contents

 * 1 Probability Theory
 * 1.1 Set Theory
 * 1.2 Basics of Probability Theory
 * 1.2.1 Axiomatic Foundations
 * 1.2.2 The Calculus of Probabilities
 * 1.2.3 Counting
 * 1.2.4 Enumerating Outcomes
 * 1.3 Conditional Probability and Independence
 * 1.4 Random Variables
 * 1.5 Distribution Functions
 * 1.6 Density and Mass Functions
 * 1.7 Exercises
 * 1.8 Miscellanea


 * 2 Transformations and Expectations
 * 2.1 Distributions of Functions of a Random Variable
 * 2.2 Expected Values
 * 2.3 Moments and Moment Generating Functions
 * 2.4 Differentiating Under an Integral Sign
 * 2.5 Exercises
 * 2.6 Miscellanea


 * 3 Common Families of Distributions
 * 3.1 Introduction
 * 3.2 Discrete Distributions
 * 3.3 Continuous Distributions
 * 3.4 Exponential Families
 * 3.5 Location and Scale Families
 * 3.6 Inequalities and Identities
 * 3.6.1 Probability Inequalities
 * 3.6.2 Identities
 * 3.7 Exercises
 * 3.8 Miscellanea


 * 4 Multiple Random Variables
 * 4.1 Joint and Marginal Distributions
 * 4.2 Conditional Distributions and Independence
 * 4.3 Bivariate Transformations
 * 4.4 Hierarchical Models and Mixture Distributions
 * 4.5 Covariance and Correlation
 * 4.6 Multivariate Distributions
 * 4.7 Inequalities
 * 4.7.1 Numerical Inequalities
 * 4.7.2 Functional Inequalities
 * 4.8 Exercises
 * 4.9 Miscellanea


 * 5 Properties of a Random Sample
 * 5.1 Basic Concepts of Random Samples
 * 5.2 Sums of Random Variables from a Random Sample
 * 5.3 Sampling from the Normal Distribution
 * 5.3.1 Properties of the Sample Mean and Variance
 * 5.3.2 The Derived Distributions: Student's $t$ and Snedecor's $F$
 * 5.4 Order Statistics
 * 5.5 Convergence Concepts
 * 5.5.1 Convergence in Probability
 * 5.5.2 Almost Sure Convergence
 * 5.5.3 Convergence in Distribution
 * 5.5.4 The Delta Method
 * 5.6 Generating a Random Sample
 * 5.6.1 Direct Methods
 * 5.6.2 Indirect Methods
 * 5.6.3 The Accept/Reject Algorithm
 * 5.7 Exercises
 * 5.8 Miscellanea


 * 6 Principles of Data Reduction
 * 6.1 Introduction
 * 6.2 The Sufficiency Principle
 * 6.2.1 Sufficient Statistics
 * 6.2.2 Minimal Sufficient Statistics
 * 6.2.3 Ancillary Statistics
 * 6.2.4 Sufficient, Ancillary and Complete Statistics
 * 6.3 The Likelihood Principle
 * 6.3.1 The Likelihood Function
 * 6.3.2 The Formal Likelihood Principle
 * 6.4 The Equivariance Principle
 * 6.5 Exercises
 * 6.6 Miscellanea


 * 7 Point Estimation
 * 7.1 Introduction
 * 7.2 Methods of Finding Estimators
 * 7.2.1 Method of Moments
 * 7.2.2 Maximum Likelihood Estimators
 * 7.2.3 Bayes Estimators
 * 7.2.4 The EM Algorithm
 * 7.3 Methods of Evaluating Estimators
 * 7.3.1 Mean Square Error
 * 7.3.2 Best Unbiased Estimators
 * 7.3.3 Sufficiency and Unbiasedness
 * 7.3.4 Loss Function Optimality
 * 7.4 Exercises
 * 7.5 Miscellanea


 * 8 Hypothesis Testing
 * 8.1 Introduction
 * 8.2 Methods of Finding Tests
 * 8.2.1 Likelihood Ratio Tests
 * 8.2.2 Bayesian Tests
 * 8.2.3 Union-Intersection and Intersection-Union Tests
 * 8.3 Methods of Evaluating Tests
 * 8.3.1 Error Probabilities and the Power Function
 * 8.3.2 Most Powerful Tests
 * 8.3.3 Sizes of Union-Intersection and Intersection-Union Tests
 * 8.3.4 p-Values
 * 8.3.5 Loss Function Optimality
 * 8.4 Exercises
 * 8.5 Miscellanea


 * 9 Interval Estimation
 * 9.1 Introduction
 * 9.2 Methods of Finding Interval Estimators
 * 9.2.1 Inverting a Test Statistic
 * 9.2.2 Pivotal Quantities
 * 9.2.3 Pivoting the CDF
 * 9.2.4 Bayesian Intervals
 * 9.3 Methods of Evaluating Interval Estimators
 * 9.3.1 Size and Coverage Probability
 * 9.3.2 Test-Related Optimality
 * 9.3.3 Bayesian Optimality
 * 9.3.4 Loss Function Optimality
 * 9.4 Exercises
 * 9.5 Miscellanea


 * 10 Asymptotic Evaluations
 * 10.1 Point Estimation
 * 10.1.1 Consistency
 * 10.1.2 Efficiency
 * 10.1.3 Calculations and Comparisons
 * 10.1.4 Bootstrap Standard Errors
 * 10.2 Robustness
 * 10.2.1 The Mean and the Median
 * 10.2.2 M-Estimators
 * 10.3 Hypothesis Testing
 * 10.3.1 Asymptotic Distribution of LRTs
 * 10.3.2 Other Large-Sample Tests
 * 10.4 Interval Estimation
 * 10.4.1 Approximate Maximum Likelihood Intervals
 * 10.4.2 Other Large-Sample Intervals
 * 10.5 Exercises
 * 10.6 Miscellanea


 * 11 Analysis of Variance and Regression
 * 11.1 Introduction
 * 11.2 Oneway Analysis of Variance
 * 11.2.1 Model and Distribution Assumptions
 * 11.2.2 The Classic ANOVA Hypothesis
 * 11.2.3 Inferences Regarding Linear Combinations of Means
 * 11.2.4 The ANOVA $F$ Test
 * 11.2.5 Simultaneous Estimation of Contrasts
 * 11.2.6 Partitioning Sums of Squares
 * 11.3 Simple Linear Regression
 * 11.3.1 Least Squares: A Mathematical Solution
 * 11.3.2 Best Linear Unbiased Estimators: A Statistical Solution
 * 11.3.3 Models and Distribution Assumptions
 * 11.3.4 Estimation and Testing with Normal Errors
 * 11.3.5 Estimation and Prediction at a Specified $x = x_0$
 * 11.3.6 Simultaneous Estimation and Confidence Bands
 * 11.4 Exercises
 * 11.5 Miscellanea


 * 12 Regression Models
 * 12.1 Introduction
 * 12.2 Regression with Errors in Variables
 * 12.2.1 Functional and Structural Relationships
 * 12.2.2 A Least Squares Solution
 * 12.2.3 Maximum Likelihood Estimation
 * 12.2.4 Confidence Sets
 * 12.3 Logistic Regression
 * 12.3.1 The Model
 * 12.3.2 Estimation
 * 12.4 Robust Regression
 * 12.5 Exercises
 * 12.6 Miscellanea


 * Appendix: Computer Algebra


 * Table of Common Distributions


 * References


 * Author Index


 * Subject Index