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Introduction to Mathematical Statistics, 8th edition

  • Robert V. Hogg, 
  • Joseph W. McKean, 
  • Allen T. Craig

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Overview

Introduction to Mathematical Statistics includes numerous illustrative examples and exercises to help you understand and retain concepts. It explores classical statistical inference procedures in estimation and testing, while drawing connections between statistical theory and practice.

Published by Pearson (August 1st 2021) - Copyright © 2019

ISBN-13: 9780137530687

Subject: Advanced Statistics

Category: Mathematical Statistics

Table of contents

Table of Contents

(Note: Sections marked with an asterisk * are optional.)

  1. Probability and Distributions
    • 1.1 Introduction
    • 1.2 Sets
    • 1.3 The Probability Set Function
    • 1.4 Conditional Probability and Independence
    • 1.5 Random Variables
    • 1.6 Discrete Random Variables
    • 1.7 Continuous Random Variables
    • 1.8 Expectation of a Random Variable
    • 1.9 Some Special Expectations
    • 1.10 Important Inequalities
  2. Multivariate Distributions
    • 2.1 Distributions of Two Random Variables
    • 2.2 Transformations: Bivariate Random Variables
    • 2.3 Conditional Distributions and Expectations
    • 2.4 Independent Random Variables
    • 2.5 The Correlation Coefficient
    • 2.6 Extension to Several Random Variables
    • 2.7 Transformations for Several Random Variables
    • 2.8 Linear Combinations of Random Variables
  3. Some Special Distributions
    • 3.1 The Binomial and Related Distributions
    • 3.2 The Poisson Distribution
    • 3.3 The Γ, χ2, and β Distributions
    • 3.4 The Normal Distribution
    • 3.5 The Multivariate Normal Distribution
    • 3.6 t- and F-Distributions
    • 3.7 Mixture Distributions*
  4. Some Elementary Statistical Inferences
    • 4.1 Sampling and Statistics
    • 4.2 Confidence Intervals
    • 4.3 ∗Confidence Intervals for Parameters of Discrete Distributions
    • 4.4 Order Statistics
    • 4.5 Introduction to Hypothesis Testing
    • 4.6 Additional Comments About Statistical Tests
    • 4.7 Chi-Square Tests
    • 4.8 The Method of Monte Carlo
    • 4.9 Bootstrap Procedures
    • 4.10 Tolerance Limits for Distributions*
  5. Consistency and Limiting Distributions
    • 5.1 Convergence in Probability
    • 5.2 Convergence in Distribution
    • 5.3 Central Limit Theorem
    • 5.4 Extensions to Multivariate Distributions*
  6. Maximum Likelihood Methods
    • 6.1 Maximum Likelihood Estimation
    • 6.2 Rao—Cramér Lower Bound and Efficiency
    • 6.3 Maximum Likelihood Tests
    • 6.4 Multiparameter Case: Estimation
    • 6.5 Multiparameter Case: Testing
    • 6.6 The EM Algorithm
  7. Sufficiency
    • 7.1 Measures of Quality of Estimators
    • 7.2 A Sufficient Statistic for a Parameter
    • 7.3 Properties of a Sufficient Statistic
    • 7.4 Completeness and Uniqueness
    • 7.5 The Exponential Class of Distributions
    • 7.6 Functions of a Parameter
    • 7.7 The Case of Several Parameters
    • 7.8 Minimal Sufficiency and Ancillary Statistics
    • 7.9 Sufficiency, Completeness, and Independence
  8. Optimal Tests of Hypotheses
    • 8.1 Most Powerful Tests
    • 8.2 Uniformly Most Powerful Tests
    • 8.3 Likelihood Ratio Tests
    • 8.3.2 Likelihood Ratio Tests for Testing Variances of Normal Distributions
    • 8.4 The Sequential Probability Ratio Test*
    • 8.5 Minimax and Classification Procedures*
  9. Inferences About Normal Linear Models
    • 9.1 Introduction
    • 9.2 One-Way ANOVA
    • 9.3 Noncentral χ2 and F-Distributions
    • 9.4 Multiple Comparisons
    • 9.5 Two-Way ANOVA
    • 9.6 A Regression Problem
    • 9.7 A Test of Independence
    • 9.8 The Distributions of Certain Quadratic Forms
    • 9.9 The Independence of Certain Quadratic Forms
  10. Nonparametric and Robust Statistics
    • 10.1 Location Models
    • 10.2 Sample Median and the Sign Test
    • 10.3 Signed-Rank Wilcoxon
    • 10.4 Mann—Whitney—Wilcoxon Procedure
    • 10.5 General Rank Scores*
    • 10.6 Adaptive Procedures*
    • 10.7 Simple Linear Model
    • 10.8 Measures of Association
    • 10.9 Robust Concepts
  11. Bayesian Statistics
    • 11.1 Bayesian Procedures
    • 11.2 More Bayesian Terminology and Ideas
    • 11.3 Gibbs Sampler
    • 11.4 Modern Bayesian Methods

Appendices:

  1. Mathematical Comments
    • A.1 Regularity Conditions
    • A.2 Sequences
  2. R Primer
    • B.1 Basics
    • B.2 Probability Distributions
    • B.3 R Functions
    • B.4 Loops
    • B.5 Input and Output
    • B.6 Packages
  3. Lists of Common Distributions
  4. Table of Distributions
  5. References
  6. Answers to Selected Exercises

Index

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