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| Probability Theory | |
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| Set Theory | |
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| Basics of Probability Theory | |
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| Axiomatic Foundations | |
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| The Calculus of Probabilities | |
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| Counting | |
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| Enumerating Outcomes | |
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| Conditional Probability and Independence | |
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| Random Variables | |
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| Distribution Functions | |
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| Density and Mass Functions | |
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| Exercises | |
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| Miscellanea | |
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| Transformations and Expectations | |
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| Distributions of Functions of a Random Variable | |
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| Expected Values | |
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| Moments and Moment Generating Functions | |
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| Differentiating Under an Integral Sign | |
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| Exercises | |
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| Miscellanea | |
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| Common Families of Distributions | |
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| Introduction | |
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| Discrete Distributions | |
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| Continuous Distributions | |
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| Exponential Families | |
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| Location and Scale Families | |
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| Inequalities and Identities | |
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| Probability Inequalities | |
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| Identities | |
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| Exercises | |
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| Miscellanea | |
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| Multiple Random Variables | |
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| Joint and Marginal Distributions | |
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| Conditional Distributions and Independence | |
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| Bivariate Transformations | |
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| Hierarchical Models and Mixture Distributions | |
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| Covariance and Correlation | |
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| Multivariate Distributions | |
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| Inequalities | |
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| Numerical Inequalities | |
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| Functional Inequalities | |
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| Exercises | |
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| Miscellanea | |
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| Properties of a Random Sample | |
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| Basic Concepts of Random Samples | |
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| Sums of Random Variables from a Random Sample | |
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| Sampling from the Normal Distribution | |
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| Properties of the Sample Mean and Variance | |
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| The Derived Distributions: Student's t and Snedecor's F | |
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| Order Statistics | |
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| Convergence Concepts | |
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| Convergence in Probability | |
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| Almost Sure Convergence | |
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| Convergence in Distribution | |
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| The Delta Method | |
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| Generating a Random Sample | |
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| Direct Methods | |
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| Indirect Methods | |
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| The Accept/Reject Algorithm | |
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| Exercises | |
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| Miscellanea | |
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| Principles of Data Reduction | |
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| Introduction | |
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| The Sufficiency Principle | |
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| Sufficient Statistics | |
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| Minimal Sufficient Statistics | |
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| Ancillary Statistics | |
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| Sufficient, Ancillary, and Complete Statistics | |
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| The Likelihood Principle | |
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| The Likelihood Function | |
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| The Formal Likelihood Principle | |
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| The Equivariance Principle | |
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| Exercises | |
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| Miscellanea | |
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| Point Estimation | |
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| Introduction | |
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| Methods of Finding Estimators | |
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| Method of Moments | |
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| Maximum Likelihood Estimators | |
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| Bayes Estimators | |
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| The EM Algorithm | |
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| Methods of Evaluating Estimators | |
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| Mean Squared Error | |
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| Best Unbiased Estimators | |
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| Sufficiency and Unbiasedness | |
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| Loss Function Optimality | |
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| Exercises | |
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| Miscellanea | |
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| Hypothesis Testing | |
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| Introduction | |
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| Methods of Finding Tests | |
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| Likelihood Ratio Tests | |
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| Bayesian Tests | |
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| Union-Intersection and Intersection-Union Tests | |
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| Methods of Evaluating Tests | |
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| Error Probabilities and the Power Function | |
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| Most Powerful Tests | |
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| Sizes of Union-Intersection and Intersection-Union Tests | |
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| p-Values | |
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| Loss Function Optimality | |
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| Exercises | |
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| Miscellanea | |
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| Interval Estimation | |
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| Introduction | |
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| Methods of Finding Interval Estimators | |
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| Inverting a Test Statistic | |
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| Pivotal Quantities | |
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| Pivoting the CDF | |
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| Bayesian Intervals | |
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| Methods of Evaluating Interval Estimators | |
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| Size and Coverage Probability | |
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| Test-Related Optimality | |
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| Bayesian Optimality | |
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| Loss Function Optimality | |
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| Exercises | |
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| Miscellanea | |
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| Asymptotic Evaluations | |
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| Point Estimation | |
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| Consistency | |
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| Efficiency | |
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| Calculations and Comparisons | |
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| Bootstrap Standard Errors | |
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| Robustness | |
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| The Mean and the Median | |
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| M-Estimators | |
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| Hypothesis Testing | |
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| Asymptotic Distribution of LRTs | |
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| Other Large-Sample Tests | |
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| Interval Estimation | |
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| Approximate Maximum Likelihood Intervals | |
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| Other Large-Sample Intervals | |
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| Exercises | |
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| Miscellanea | |
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| Analysis of Variance and Regression | |
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| Introduction | |
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| Oneway Analysis of Variance | |
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| Model and Distribution Assumptions | |
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| The Classic ANOVA Hypothesis | |
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| Inferences Regarding Linear Combinations of Means | |
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| The ANOVA F Test | |
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| Simultaneous Estimation of Contrasts | |
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| Partitioning Sums of Squares | |
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| Simple Linear Regression | |
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| Least Squares: A Mathematical Solution | |
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| Best Linear Unbiased Estimators: A Statistical Solution | |
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| Models and Distribution Assumptions | |
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| Estimation and Testing with Normal Errors | |
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| Estimation and Prediction at a Specified x = x[subscript 0] | |
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| Simultaneous Estimation and Confidence Bands | |
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| Exercises | |
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| Miscellanea | |
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| Regression Models | |
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| Introduction | |
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| Regression with Errors in Variables | |
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| Functional and Structural Relationships | |
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| A Least Squares Solution | |
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| Maximum Likelihood Estimation | |
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| Confidence Sets | |
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| Logistic Regression | |
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| The Model | |
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| Estimation | |
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| Robust Regression | |
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| Exercises | |
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| Miscellanea | |
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| Computer Algebra | |
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| Table of Common Distributions | |
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| References | |
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| Author Index | |
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| Subject Index | |