Solution manual for Introduction to Mathematical Statistics 8th Edition by Robert Hogg,Joseph McKean,Allen Craig 9780134686998 0134686993

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ISBN 10:0134686993
ISBN 13:9780134686998
Author:Robert Hogg,Joseph McKean,Allen Craig
This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. For courses in mathematical statistics. Comprehensive coverage of mathematical statistics — with a proven approach Introduction to Mathematical Statistics by Hogg, McKean, and Craig enhances student comprehension and retention with numerous, illustrative examples and exercises. Classical statistical inference procedures in estimation and testing are explored extensively, and the text’s flexible organization makes it ideal for a range of mathematical statistics courses. Substantial changes to the 8th Edition — many based on user feedback — help students appreciate the connection between statistical theory and statistical practice, while other changes enhance the development and discussion of the statistical theory presented.

Introduction to Mathematical Statistics 8th Table of contents:

Chapter 1 Probability and Distributions

1.1 Introduction

1.2 Sets

1.2.1 Review of Set Theory

1.2.2 Set Functions

Exercises

1.3 The Probability Set Function

1.3.1 Counting Rules

1.3.2 Additional Properties of Probability

Exercises

1.4 Conditional Probability and Independence

1.4.1 Independence

1.4.2 Simulations

Exercises

1.5 Random Variables

Exercises

1.6 Discrete Random Variables

1.6.1 Transformations

Exercises

1.7 Continuous Random Variables

1.7.1 Quantiles

1.7.2 Transformations

1.7.3 Mixtures of Discrete and Continuous Type Distributions

Exercises

1.8 Expectation of a Random Variable

1.8.1 R Computation for an Estimation of the Expected Gain

Exercises

1.9 Some Special Expectations

Exercises

1.10 Important Inequalities

Exercises

Chapter 2 Multivariate Distributions

2.1 Distributions of Two Random Variables

2.1.1 Marginal Distributions

2.1.2 Expectation

Exercises

2.2 Transformations: Bivariate Random Variables

Exercises

2.3 Conditional Distributions and Expectations

Exercises

2.4 Independent Random Variables

Exercises

2.5 The Correlation Coefficient

Exercises

2.6 Extension to Several Random Variables

2.6.1 *Multivariate Variance-Covariance Matrix

Exercises

2.7 Transformations for Several Random Variables

Exercises

2.8 Linear Combinations of Random Variables

Exercises

Chapter 3 Some Special Distributions

3.1 The Binomial and Related Distributions

3.1.1 Negative Binomial and Geometric Distributions

3.1.2 Multinomial Distribution

3.1.3 Hypergeometric Distribution

Exercises

3.2 The Poisson Distribution

Exercises

3.3 The Γ, χ2, and β Distributions

3.3.1 The χ2-Distribution

3.3.2 The β-Distribution

Exercises

3.4 The Normal Distribution

3.4.1 *Contaminated Normals

Exercises

3.5 The Multivariate Normal Distribution

3.5.1 Bivariate Normal Distribution

3.5.2 *Multivariate Normal Distribution, General Case

3.5.3 *Applications

Exercises

3.6 t- and F-Distributions

3.6.1 The t-distribution

3.6.2 The F-distribution

3.6.3 Student’s Theorem

Exercises

3.7 *Mixture Distributions

Exercises

Chapter 4 Some Elementary Statistical Inferences

4.1 Sampling and Statistics

4.1.1 Point Estimators

4.1.2 Histogram Estimates of pmfs and pdfs

The distribution of X is discrete

The Distribution of X Is Continuous

Exercises

4.2 Confidence Intervals

4.2.1 Confidence Intervals for Difference in Means

4.2.2 Confidence Interval for Difference in Proportions

Exercises

4.3 *Confidence Intervals for Parameters of Discrete Distributions

Numerical Illustration

Numerical Illustration

Exercises

4.4 Order Statistics

4.4.1 Quantiles

4.4.2 Confidence Intervals for Quantiles

Exercises

4.5 Introduction to Hypothesis Testing

Exercises

4.6 Additional Comments About Statistical Tests

4.6.1 Observed Significance Level, p-value

Exercises

4.7 Chi-Square Tests

Exercises

4.8 The Method of Monte Carlo

4.8.1 Accept–Reject Generation Algorithm

Exercises

4.9 Bootstrap Procedures

4.9.1 Percentile Bootstrap Confidence Intervals

4.9.2 Bootstrap testing procedures

Exercises

4.10 *Tolerance Limits for Distributions

Exercises

Chapter 5 Consistency and Limiting Distributions

5.1 Convergence in Probability

5.1.1 Sampling and Statistics

Exercises

5.2 Convergence in Distribution

5.2.1 Bounded in Probability

5.2.2 ∆-Method

5.2.3 Moment Generating Function Technique

Exercises

5.3 Central Limit Theorem

Exercises

5.4 *Extensions to Multivariate Distributions

Exercises

Chapter 6 Maximum Likelihood Methods

6.1 Maximum Likelihood Estimation

Exercises

6.2 Rao–Cramér Lower Bound and Efficiency

Exercises

6.3 Maximum Likelihood Tests

Exercises

6.4 Multiparameter Case: Estimation

Exercises

6.5 Multiparameter Case: Testing

Exercises

6.6 The EM Algorithm

Exercises

Chapter 7 Sufficiency

7.1 Measures of Quality of Estimators

Exercises

7.2 A Sufficient Statistic for a Parameter

Exercises

7.3 Properties of a Sufficient Statistic

Exercises

7.4 Completeness and Uniqueness

Exercises

7.5 The Exponential Class of Distributions

Exercises

7.6 Functions of a Parameter

7.6.1 Bootstrap Standard Errors

Exercises

7.7 The Case of Several Parameters

Exercises

7.8 Minimal Sufficiency and Ancillary Statistics

Exercises

7.9 Sufficiency, Completeness, and Independence

Exercises

Chapter 8 Optimal Tests of Hypotheses

8.1 Most Powerful Tests

Exercises

8.2 Uniformly Most Powerful Tests

Exercises

8.3 Likelihood Ratio Tests

8.3.1 Likelihood Ratio Tests for Testing Means of Normal Distributions

8.3.2 Likelihood Ratio Tests for Testing Variances of Normal Distributions

Exercises

8.4 *The Sequential Probability Ratio Test

Exercises

8.5 *Minimax and Classification Procedures

8.5.1 Minimax Procedures

8.5.2 Classification

Exercises

Chapter 9 Inferences About Normal Linear Models

9.1 Introduction

9.2 One-Way ANOVA

Exercises

9.3 Noncentral χ2 and F-Distributions

Exercises

9.4 Multiple Comparisons

9.5 Two-Way ANOVA

9.5.1 Interaction between Factors

Exercises

9.6 A Regression Problem

9.6.1 Maximum Likelihood Estimates

9.6.2 *Geometry of the Least Squares Fit

Exercises

9.7 A Test of Independence

Exercises

9.8 The Distributions of Certain Quadratic Forms

Exercises

9.9 The Independence of Certain Quadratic Forms

Exercises

Chapter 10 Nonparametric and Robust Statistics

10.1 Location Models

Exercises

10.2 Sample Median and the Sign Test

10.2.1 Asymptotic Relative Efficiency

10.2.2 Estimating Equations Based on the Sign Test

10.2.3 Confidence Interval for the Median

Exercises

10.3 Signed-Rank Wilcoxon

10.3.1 Asymptotic Relative Efficiency

10.3.2 Estimating Equations Based on Signed-Rank Wilcoxon

10.3.3 Confidence Interval for the Median

10.3.4 Monte Carlo Investigation

Exercises

10.4 Mann–Whitney–Wilcoxon Procedure

10.4.1 Asymptotic Relative Efficiency

10.4.2 Estimating Equations Based on the Mann–Whitney–Wilcoxon

10.4.3 Confidence Interval for the Shift Parameter Δ

10.4.4 Monte Carlo Investigation of Power

Exercises

10.5 * General Rank Scores

10.5.1 Efficacy

10.5.2 Estimating Equations Based on General Scores

10.5.3 Optimization: Best Estimates

Exercises

10.6 *Adaptive Procedures

Exercises

10.7 Simple Linear Model

Exercises

10.8 Measures of Association

10.8.1 Kendall’s τ

10.8.2 Spearman’s Rho

Exercises

10.9 Robust Concepts

10.9.1 Location Model

Influence Functions

Breakdown Point of an Estimator

10.9.2 Linear Model

Least Squares and Wilcoxon Procedures

Influence Functions

Breakdown Points

Intercept

Exercises

Endnotes

Chapter 11 Bayesian statistics

11.1 Bayesian Procedures

11.1.1 Prior and Posterior Distributions

11.1.2 Bayesian Point Estimation

11.1.3 Bayesian Interval Estimation

11.1.4 Bayesian Testing Procedures

11.1.5 Bayesian Sequential Procedures

Exercises

11.2 More Bayesian Terminology and Ideas

Exercises

11.3 Gibbs sampler

Exercises

11.4 Modern bayesian methods

11.4.1 Empirical bayes

Exercises

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