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Mathematical Statistics with Resampling and R, 2nd Edition

Mathematical Statistics with Resampling and R, 2nd Edition

Laura M. Chihara, Tim C. Hesterberg

ISBN: 978-1-119-41654-8

Aug 2018

592 pages




This thoroughly updated second edition combines the latest software applications with the benefits of modern resampling techniques

Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. The second edition of Mathematical Statistics with Resampling and R combines modern resampling techniques and mathematical statistics. This book has been classroom-tested to ensure an accessible presentation, uses the powerful and flexible computer language R for data analysis and explores the benefits of modern resampling techniques.

This book offers an introduction to permutation tests and bootstrap methods that can serve to motivate classical inference methods. The book strikes a balance between theory, computing, and applications, and the new edition explores additional topics including consulting, paired t test, ANOVA and Google Interview Questions. Throughout the book, new and updated case studies are included representing a diverse range of subjects such as flight delays, birth weights of babies, and telephone company repair times. These illustrate the relevance of the real-world applications of the material. This new edition:

•    Puts the focus on statistical consulting that emphasizes giving a client an understanding of data and goes beyond typical expectations

•    Presents new material on topics such as the paired t test, Fisher's Exact Test and the EM algorithm

•    Offers a new section on "Google Interview Questions" that illustrates statistical thinking

•    Provides a new chapter on ANOVA

•    Contains more exercises and updated case studies, data sets, and R code 

Written for undergraduate students in a mathematical statistics course as well as practitioners and researchers, the second edition of Mathematical Statistics with Resampling and R presents a revised and updated guide for applying the most current resampling techniques to mathematical statistics.

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Chapter 1: Data and Case Studies

1.1 Case study: Flight Delays

1.2 Case Study: Birth Weights of Babies

1.3 Case Study: Verizon Repair Times

1.4 Case Study: Iowa Recidivism

1.5 Sampling

1.6 Parameters and Statistics

1.7 Case Study: General Social Survey

1.8 Sample Surveys

1.9 Case Study: Beer and Hot Wings

1.10 Case Study: Black Spruce Seedlings

1.11 Studies

1.12 Google Interview Question—Mobile Ads Optimization


Chapter 2: Exploratory Data Analysis 2

2.1 Basic Plots

2.2 Numeric Summaries

2.2.1 Center

2.2.2 Spread

2.2.3 Shape

2.3 Boxplots

2.4 Quantiles and Normal Quantile Plots

2.5 Empirical Cumulative Distribution Functions

2.6 Scatter Plots

2.7 Skewness and kurtosis


Chapter 3: Introduction to Hypothesis Testing: Permutation Tests

3.1 Introduction to Hypothesis Testing

3.2 Hypotheses

3.3 Permutation Tests

3.3.1 Implementation issues

3.3.2 One-sided and two-sided tests

3.3.3 Other statistics

3.3.4 Assumptions

3.3.5 Remark on Terminology

3.4 Matched Pairs


Chapter 4: Sampling Distributions

4.1 Sampling Distributions

4.2 Calculating Sampling Distributions

4.3 The Central Limit Theorem

4.3.1 CLT for Binomial Data

4.3.2 Continuity Correction for Discrete Random Variables

4.3.3 Accuracy of the Central Limit Theorem*

4.3.4 CLT for Sampling without Replacement


Chapter 5: Introduction to Confidence Intervals: The Bootstrap

5.1 Introduction to the Bootstrap

5.2 The Plug-In Principle

5.2.1 Estimating the Population Distribution

5.2.2 How Useful Is the Bootstrap Distribution?

5.3 Bootstrap Percentile Intervals

5.4 Two Sample Bootstrap

5.5 Other Statistics

5.6 Bias

5.7 Monte Carlo Sampling: the “Second Bootstrap Principle”

5.8 Accuracy of Bootstrap Distributions

5.8.1 Sample Mean, Large Sample Size:

5.8.2 Sample Mean: Small Sample Size

5.8.3 Sample Median

5.8.4 Mean Variance Relationship

5.9 How many bootstrap samples are needed?


Chapter 6: Estimation

6.1 Maximum Likelihood Estimation

6.1.1 Maximum Likelihood for Discrete Distributions

6.1.2 Maximum Likelihood for Continuous Distributions

6.1.3 Maximum Likelihood for Multiple Parameters

6.2 Method of Moments

6.3 Properties of Estimators

6.3.1 Unbiasedness

6.3.2 Efficiency

6.3.3 Mean Square Error

6.3.4 Consistency

6.3.5 Transformation Invariance*

6.3.6 Asymptotic Normality of MLE*

6.4 Statistical Practice


Chapter 7: More Confidence Intervals

7.1 Confidence Intervals for Means

7.1.1 Confidence Intervals for a Mean, Variance Known

7.1.2 Confidence Intervals for a Mean, Variance Unknown

7.1.3 Confidence Intervals for a Difference in Means

7.1.4 Matched Pairs, revisited

7.2 Confidence Intervals in General

7.2.1 Location and Scale Parameters*

7.3 One-Sided Confidence Intervals

7.4 Confidence Intervals for Proportions

7.4.1 The Agresti-Coull Interval for a Proportion

7.4.2 Confidence Interval for the Difference of Proportions

7.5 Bootstrap Confidence Intervals

7.5.1 t Confidence Interval using Bootstrap Standard Error

7.5.2 Bootstrap t Confidence Intervals

7.5.3 Comparing Bootstrap t and Formula t Confidence Intervals

7.6 Confidence Interval Properties


Chapter 8: More Hypothesis Testing

8.1 Hypothesis Tests for Means and Proportions: One Population

8.1.1 A Single Mean

8.1.2 One Proportion

8.2 Bootstrap T Tests

8.3 Hypothesis Tests for Means and Proportions: Two Populations

8.3.1 Comparing Two Means

8.3.2 Comparing Two Proportions

8.4 Type I and Type II errors

8.4.1 Type I errors

8.4.2 Type II errors and power

8.4.3 P-Values versus Critical Regions

8.5 Interpreting Test Results

8.5.1 P-values

8.5.2 On Significance

8.5.3 Adjustments for Multiple Testing

8.6 Likelihood Ratio Tests

8.6.1 Simple Hypotheses and the Neyman–Pearson Lemma

8.6.2 Likelihood Ratio Tests for Composite Hypotheses

8.7 Statistical Practice


Chapter 9: Regression

9.1 Covariance

9.2 Correlation

9.3 Least Squares Regression

9.3.1 Regression toward the Mean

9.3.2 Variation

9.3.3 Diagnostics

9.3.4 Multiple Regression

9.4 The Simple Linear Model

9.4.1 Inference for α and β

9.4.2 Inference for the Response

9.4.3 Comments about Assumptions for the Linear Model

9.5 Resampling Correlation and Regression

9.6 Logistic Regression

9.6.1 Inference for Logistic Regression


Chapter 10: Categorical Data

10.1 Independence in Contingency Tables

10.2 Permutation Test of Independence

10.3 Chi-Square Test of Independence

10.3.1 Model for Chi-Square Test of Independence

10.3.2 2 x 2 Tables

10.3.3 Fisher’s Exact Test

10.3.4 Conditioning

10.4 Chi-Square Test of Homogeneity

10.5 Goodness-of-Fit Tests

10.5.1 All Parameters Known

10.5.2 Some Parameters Estimated

10.6 Chi-square and the likelihood ratio*


Chapter 11: Bayesian Methods

11.1 Bayes Theorem

11.2 Binomial Data, Discrete Prior Distributions

11.3 Binomial Data, Continuous Prior Distributions

11.4 Continuous Data

11.5 Sequential Data


Chapter 12 One-Way ANOVA

12.1 Comparing three or more populations

12.1.1 The ANOVA F Test

12.1.2 A Permutation Test Approach


Chapter 13: Additional Topics

13.1 Smoothed Bootstrap

13.1.1 Kernel Density Estimate

13.2 Parametric Bootstrap

13.3 The Delta Method

13.4 Stratified Sampling

13.5 Computational Issues in Bayesian Analysis

13.6 Monte Carlo Integration

13.7 Importance Sampling

13.7.1 Ratio Estimate for Importance Sampling

13.7.2 Importance Sampling in Bayesian Applications

13.8 The EM Algorithm

13.8.1 General Background


A Review of Probability

A.1 Basic Probability

A.2 Mean and Variance

A.3 The Normal Distribution

A.4 The Mean of a Sample of Random Variables

A.5 Sums of Normal Random Variables

A.6 The Law of Averages

A.7 Higher moments and the moment generating function

B Probability Distributions

B.1 The Bernoulli and Binomial Distributions

B.2 The Multinomial Distribution

B.3 The Geometric Distribution

B.4 The Negative Binomial Distribution

B.5 The Hypergeometric Distribution

B.6 The Poisson Distribution

B.7 The Uniform Distribution

B.8 The Exponential Distribution

B.9 The Gamma Distribution

B.10 The Chi-square Distribution

B.11 The Student’s t Distribution

B.12 The Beta Distribution

B.13 The F Distribution


C Distributions Quick Reference

Problem Solutions