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Statistical Inference

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ISBN-10: 0534243126

ISBN-13: 9780534243128

Edition: 2nd 2002 (Revised)

Authors: George Casella, Roger L. Berger

List price: $331.95
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Description:

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…    
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Book details

List price: $331.95
Edition: 2nd
Copyright year: 2002
Publisher: Brooks/Cole
Publication date: 6/18/2001
Binding: Hardcover
Pages: 688
Size: 6.50" wide x 9.25" long x 1.25" tall
Weight: 2.288
Language: English

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