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Statistical Inference

Statistical Inference - 2nd edition

ISBN13: 978-0534243128

Cover of Statistical Inference 2ND 02 (ISBN 978-0534243128)
ISBN13: 978-0534243128
ISBN10: 0534243126
Cover type: Hardback
Edition/Copyright: 2ND 02
Publisher: Duxbury Press
Published: 2002
International: No
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Statistical Inference - 2ND 02 edition

ISBN13: 978-0534243128

George Casella and Roger L. Berger

ISBN13: 978-0534243128
ISBN10: 0534243126
Cover type: Hardback
Edition/Copyright: 2ND 02
Publisher: Duxbury Press

Published: 2002
International: No
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