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by George Casella and Roger L. Berger

Cover type: HardbackEdition: 2ND 02

Copyright: 2002

Publisher: Duxbury Press

Published: 2002

International: No

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This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

**Benefits: **

- Begins with the basics of probability theory and introduces many fundamentals that are later necessary (Chapters 1-4).
- NEW! Gathers all large sample results into Chapter 10.
- NEW! Includes a new section on "Generating a Random Sample" in Chapter 5.
- NEW! Includes new sections on "Logistic Regression" and "Robust Regression" in Chapter 12.
- NEW! Contains updated and expanded Exercises in all chapters, and updated and expanded Miscellanea including discussions of variations on likelihood and Bayesian analysis, bootstrap, "second-order" asymptotics, and Monte Carlo Markov chain.
- NEW! Contains an Appendix detailing the use of Mathematica in problem solving.
- Treats likelihood and sufficiency principles in detail. These principles, and the thinking behind them, are fundamental to total statistical understanding. The equivariance principle is also introduced.
- Divides the methods of finding appropriate statistical methods and the methods of evaluating these techniques in the core statistical inference chapters (Chapters 7-9). Integrates decision theoretic evaluations into core chapters. Many of the techniques are used in consulting and are helpful in analyzing and inferring from actual problems.
- Discusses use of simulation in mathematical statistics.
- Includes a thorough introduction to large sample statistical methods.
- Covers the elementary linear models through simple linear regression and oneway analysis of variance.
- Covers more advanced theory of regression topics including "errors in variables" regression, logistic regression, and robust regression.
- NEW! Offers new coverage of random number generation, simulation methods, bootstrapping, EM algorithm, p-values, and robustness.
- NEW! Restructures material for clarity purposes.

**Casella, George : Cornell University**

**Berger,Roger L.: North Carolina State University**

**1. PROBABILITY THEORY**

Set Theory

Probability Theory

Conditional Probability and Independence

Random Variables

Distribution Functions

Density and Mass Functions

Exercises

Miscellanea

**2. TRANSFORMATION AND EXPECTATIONS**

Distribution of Functions of a Random Variable

Expected Values

Moments and Moment Generating Functions

Differentiating Under an Integral Sign

Exercises

Miscellanea

**3. COMMON FAMILIES OF DISTRIBUTIONS**

Introductions

Discrete Distributions

Continuous Distributions

Exponential Families

Locations and Scale Families

Inequalities and Identities

Exercises

Miscellanea

**4. MULTIPLE RANDOM VARIABLES**

Joint and Marginal Distributions

Conditional Distributions and Independence

Bivariate Transformations

Hierarchical Models and Mixture Distributions

Covariance and Correlation

Multivariate Distributions

Inequalities

Exercises

Miscellanea

**5. PROPERTIES OF A RANDOM SAMPLE**

Basic Concepts of Random Samples

Sums of Random Variables from a Random Sample

Sampling for the Normal Distribution

Order Statistics

Convergence Concepts

Generating a Random Sample

Exercises

Miscellanea

**6. PRINCIPLES OF DATA REDUCTION**

Introduction

The Sufficiency Principle

The Likelihood Principle

The Equivariance Principle

Exercises

Miscellanea

**7. POINT EXTIMATION**

Introduction

Methods of Finding Estimators

Methods of Evaluating Estimators

Exercises

Miscellanea

**8. HYPOTHESIS TESTING**

Introduction

Methods of Finding Tests

Methods of Evaluating Test

Exercises

Miscellanea

**9. INTERVAL ESTIMATION**

Introduction

Methods of Finding Interval Estimators

Methods of Evaluating Interval Estimators

Exercises

Miscellanea

**10. ASYMPTOTIC EVALUATIONS**

Point Estimation

Robustness

Hypothesis Testing

Interval Estimation

Exercises

Miscellanea

**11. ANALYSIS OF VARIANCE AND REGRESSION**

Introduction

One-way Analysis of Variance

Simple Linear Regression

Exercises

Miscellanea

**12. REGRESSION MODELS**

Introduction

Regression with Errors in Variables

Logistic Regression

Robust Regression

Exercises

Miscellanea

Appendix

Computer Algebra

References

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Summary

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

**Benefits: **

- Begins with the basics of probability theory and introduces many fundamentals that are later necessary (Chapters 1-4).
- NEW! Gathers all large sample results into Chapter 10.
- NEW! Includes a new section on "Generating a Random Sample" in Chapter 5.
- NEW! Includes new sections on "Logistic Regression" and "Robust Regression" in Chapter 12.
- NEW! Contains updated and expanded Exercises in all chapters, and updated and expanded Miscellanea including discussions of variations on likelihood and Bayesian analysis, bootstrap, "second-order" asymptotics, and Monte Carlo Markov chain.
- NEW! Contains an Appendix detailing the use of Mathematica in problem solving.
- Treats likelihood and sufficiency principles in detail. These principles, and the thinking behind them, are fundamental to total statistical understanding. The equivariance principle is also introduced.
- Divides the methods of finding appropriate statistical methods and the methods of evaluating these techniques in the core statistical inference chapters (Chapters 7-9). Integrates decision theoretic evaluations into core chapters. Many of the techniques are used in consulting and are helpful in analyzing and inferring from actual problems.
- Discusses use of simulation in mathematical statistics.
- Includes a thorough introduction to large sample statistical methods.
- Covers the elementary linear models through simple linear regression and oneway analysis of variance.
- Covers more advanced theory of regression topics including "errors in variables" regression, logistic regression, and robust regression.
- NEW! Offers new coverage of random number generation, simulation methods, bootstrapping, EM algorithm, p-values, and robustness.
- NEW! Restructures material for clarity purposes.

Author Bio

**Casella, George : Cornell University**

**Berger,Roger L.: North Carolina State University**

Table of Contents

**1. PROBABILITY THEORY**

Set Theory

Probability Theory

Conditional Probability and Independence

Random Variables

Distribution Functions

Density and Mass Functions

Exercises

Miscellanea

**2. TRANSFORMATION AND EXPECTATIONS**

Distribution of Functions of a Random Variable

Expected Values

Moments and Moment Generating Functions

Differentiating Under an Integral Sign

Exercises

Miscellanea

**3. COMMON FAMILIES OF DISTRIBUTIONS**

Introductions

Discrete Distributions

Continuous Distributions

Exponential Families

Locations and Scale Families

Inequalities and Identities

Exercises

Miscellanea

**4. MULTIPLE RANDOM VARIABLES**

Joint and Marginal Distributions

Conditional Distributions and Independence

Bivariate Transformations

Hierarchical Models and Mixture Distributions

Covariance and Correlation

Multivariate Distributions

Inequalities

Exercises

Miscellanea

**5. PROPERTIES OF A RANDOM SAMPLE**

Basic Concepts of Random Samples

Sums of Random Variables from a Random Sample

Sampling for the Normal Distribution

Order Statistics

Convergence Concepts

Generating a Random Sample

Exercises

Miscellanea

**6. PRINCIPLES OF DATA REDUCTION**

Introduction

The Sufficiency Principle

The Likelihood Principle

The Equivariance Principle

Exercises

Miscellanea

**7. POINT EXTIMATION**

Introduction

Methods of Finding Estimators

Methods of Evaluating Estimators

Exercises

Miscellanea

**8. HYPOTHESIS TESTING**

Introduction

Methods of Finding Tests

Methods of Evaluating Test

Exercises

Miscellanea

**9. INTERVAL ESTIMATION**

Introduction

Methods of Finding Interval Estimators

Methods of Evaluating Interval Estimators

Exercises

Miscellanea

**10. ASYMPTOTIC EVALUATIONS**

Point Estimation

Robustness

Hypothesis Testing

Interval Estimation

Exercises

Miscellanea

**11. ANALYSIS OF VARIANCE AND REGRESSION**

Introduction

One-way Analysis of Variance

Simple Linear Regression

Exercises

Miscellanea

**12. REGRESSION MODELS**

Introduction

Regression with Errors in Variables

Logistic Regression

Robust Regression

Exercises

Miscellanea

Appendix

Computer Algebra

References

Publisher Info

Publisher: Duxbury Press

Published: 2002

International: No

Published: 2002

International: No

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

**Benefits: **

- Begins with the basics of probability theory and introduces many fundamentals that are later necessary (Chapters 1-4).
- NEW! Gathers all large sample results into Chapter 10.
- NEW! Includes a new section on "Generating a Random Sample" in Chapter 5.
- NEW! Includes new sections on "Logistic Regression" and "Robust Regression" in Chapter 12.
- NEW! Contains updated and expanded Exercises in all chapters, and updated and expanded Miscellanea including discussions of variations on likelihood and Bayesian analysis, bootstrap, "second-order" asymptotics, and Monte Carlo Markov chain.
- NEW! Contains an Appendix detailing the use of Mathematica in problem solving.
- Treats likelihood and sufficiency principles in detail. These principles, and the thinking behind them, are fundamental to total statistical understanding. The equivariance principle is also introduced.
- Divides the methods of finding appropriate statistical methods and the methods of evaluating these techniques in the core statistical inference chapters (Chapters 7-9). Integrates decision theoretic evaluations into core chapters. Many of the techniques are used in consulting and are helpful in analyzing and inferring from actual problems.
- Discusses use of simulation in mathematical statistics.
- Includes a thorough introduction to large sample statistical methods.
- Covers the elementary linear models through simple linear regression and oneway analysis of variance.
- Covers more advanced theory of regression topics including "errors in variables" regression, logistic regression, and robust regression.
- NEW! Offers new coverage of random number generation, simulation methods, bootstrapping, EM algorithm, p-values, and robustness.
- NEW! Restructures material for clarity purposes.

**Casella, George : Cornell University**

**Berger,Roger L.: North Carolina State University**

**1. PROBABILITY THEORY**

Set Theory

Probability Theory

Conditional Probability and Independence

Random Variables

Distribution Functions

Density and Mass Functions

Exercises

Miscellanea

**2. TRANSFORMATION AND EXPECTATIONS**

Distribution of Functions of a Random Variable

Expected Values

Moments and Moment Generating Functions

Differentiating Under an Integral Sign

Exercises

Miscellanea

**3. COMMON FAMILIES OF DISTRIBUTIONS**

Introductions

Discrete Distributions

Continuous Distributions

Exponential Families

Locations and Scale Families

Inequalities and Identities

Exercises

Miscellanea

**4. MULTIPLE RANDOM VARIABLES**

Joint and Marginal Distributions

Conditional Distributions and Independence

Bivariate Transformations

Hierarchical Models and Mixture Distributions

Covariance and Correlation

Multivariate Distributions

Inequalities

Exercises

Miscellanea

**5. PROPERTIES OF A RANDOM SAMPLE**

Basic Concepts of Random Samples

Sums of Random Variables from a Random Sample

Sampling for the Normal Distribution

Order Statistics

Convergence Concepts

Generating a Random Sample

Exercises

Miscellanea

**6. PRINCIPLES OF DATA REDUCTION**

Introduction

The Sufficiency Principle

The Likelihood Principle

The Equivariance Principle

Exercises

Miscellanea

**7. POINT EXTIMATION**

Introduction

Methods of Finding Estimators

Methods of Evaluating Estimators

Exercises

Miscellanea

**8. HYPOTHESIS TESTING**

Introduction

Methods of Finding Tests

Methods of Evaluating Test

Exercises

Miscellanea

**9. INTERVAL ESTIMATION**

Introduction

Methods of Finding Interval Estimators

Methods of Evaluating Interval Estimators

Exercises

Miscellanea

**10. ASYMPTOTIC EVALUATIONS**

Point Estimation

Robustness

Hypothesis Testing

Interval Estimation

Exercises

Miscellanea

**11. ANALYSIS OF VARIANCE AND REGRESSION**

Introduction

One-way Analysis of Variance

Simple Linear Regression

Exercises

Miscellanea

**12. REGRESSION MODELS**

Introduction

Regression with Errors in Variables

Logistic Regression

Robust Regression

Exercises

Miscellanea

Appendix

Computer Algebra

References