Mathematical Statistics with Resampling and R

Mathematical Statistics with Resampling and R This thoroughly updated third 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 third edition of Mathematical Statistics with Resampling and R combines modern resampling techniques and mathematical statistics. This book is classroom-tested to ensure an accessible presentation, and uses the powerful and flexible computer language R for data analysis. This book introduces permutation tests and bootstrap methods to motivate classical inference methods, as well as to be utilized as useful tools in their own right when classical methods are inaccurate or unavailable. The book strikes a balance between simulation, computing, theory, data, and applications. Throughout the book, new and updated case studies representing a diverse range of subjects, such as flight delays, birth weights of babies, U.S. demographics, views on sociological issues, and problems at Google and Instacart, illustrate the relevance of mathematical statistics to real-world applications. Changes and additions to the third edition include: New and updated case studies that incorporate contemporary subjects like COVID-19 Several new sections, including introductory material on causal models and regression methods for causal modeling in practice Modern terminology distinguishing statistical discernibility and practical importance New exercises and examples, data sets, and R code, using dplyr and ggplot2 A complete instructor’s solutions manual A new github site that contains code, data sets, additional topics, and instructor resources Mathematical Statistics with Resampling and R is an ideal textbook for undergraduate and graduate students in mathematical statistics courses, as well as practitioners and researchers looking to expand their toolkit of resampling and classical techniques.

Table of Contents:
Preface xiii 1 Data and Case Studies 1 1.1 Case Study: Flight Delays 1 1.2 Case Study: BirthWeights of Babies 2 1.3 Case Study: Verizon Repair Times 3 1.4 Case Study: Iowa Recidivism 4 1.5 Sampling 5 1.6 Parameters and Statistics 6 1.7 Case Study: General Social Survey 7 1.8 Sample Surveys 8 1.9 Case Study: Beer and HotWings 9 1.10 Case Study: Black Spruce Seedlings 10 1.11 Studies 11 1.12 Google Interview Question: Mobile Ads Optimization 13 2 Exploratory Data Analysis 21 2.1 Basic Plots 21 2.2 Numeric Summaries 25 2.3 Boxplots 27 2.4 Quantiles and Normal Quantile Plots 29 2.5 Empirical Cumulative Distribution Functions 34 2.6 Scatter Plots 36 2.7 Skewness and Kurtosis 38 3 Introduction to Hypothesis Testing: Permutation Tests 45 3.1 Introduction to Hypothesis Testing 45 3.2 Hypotheses 46 3.3 Permutation Tests 50 3.4 Matched Pairs 66 3.5 Cause and Effect 67 4 Sampling Distributions 77 4.1 Sampling Distributions 77 4.2 Calculating Sampling Distributions 82 4.3 The Central LimitTheorem 85 5 Introduction to Confidence Intervals: The Bootstrap 103 5.1 Introduction to the Bootstrap 103 5.2 The Plug-in Principle 109 5.3 Bootstrap Percentile Intervals 115 5.4 Two Sample Bootstrap 116 5.5 Other Statistics 123 5.6 Bias 126 5.7 Monte Carlo Sampling 130 5.8 Accuracy of Bootstrap Distributions 131 5.9 How Many Bootstrap Samples Are Needed? 136 6 Estimation 147 6.1 Maximum Likelihood Estimation 147 6.2 Method of Moments 158 6.3 Properties of Estimators 160 6.4 Statistical Practice 174 7 More Confidence Intervals 183 7.1 Confidence Intervals for Means 183 7.2 Confidence Intervals Using Pivots 201 7.3 One-Sided Confidence Intervals 209 7.4 Confidence Intervals for Proportions 211 7.5 Bootstrap Confidence Intervals 216 7.6 Confidence Interval Properties 224 7.7 The Delta Method* 226 8 More Hypothesis Testing 245 8.1 Hypothesis Tests for Means and Proportions: One Population 245 8.2 Bootstrap t Tests 250 8.3 Hypothesis Tests for Means and Proportions: Two Populations 252 8.4 Type I and Type II Errors 261 8.5 Interpreting Test Results 276 8.6 Likelihood Ratio Tests 281 8.7 Statistical Practice 289 9 Regression 309 9.1 Covariance 309 9.2 Correlation 313 9.3 Least Squares Regression 316 9.4 The Simple LinearModel 329 9.5 Resampling Correlation and Regression 342 9.6 Logistic Regression 350 10 Categorical Data 367 10.1 Independence in Contingency Tables 367 10.2 Permutation Test of Independence 369 10.3 Chi-Square Test of Independence 371 10.4 Chi-Square Test of Homogeneity 380 10.5 Goodness-of-Fit Tests 382 10.6 Chi-Square and the Likelihood Ratio* 388 11 Bayesian Methods 399 11.1 Bayes Theorem 400 11.2 Binomial Data: Discrete Prior Distributions 400 11.3 Binomial Data: Continuous Prior Distributions 408 11.4 Continuous Data 414 11.5 Sequential Data 417 12 One-Way ANOVA 429 12.1 Comparing Three or More Populations 429 13 Additional Topics 443 13.1 Smoothed Bootstrap 444 13.2 Parametric Bootstrap 449 13.3 Stratified Sampling 452 13.4 Control Variates and Casual Modeling 455 13.5 Computational Issues in Bayesian Analysis 462 13.6 Monte Carlo Integration 464 13.7 Importance Sampling 468 13.8 The EM Algorithm 483 Appendix A Review of Probability 493 A.1 Basic Probability 493 A.2 Mean and Variance 494 A.3 Marginal and Conditional Distributions 496 A.4 The Normal Distribution 497 A.5 The Mean of a Sample of Random Variables 498 A.6 Sums of Normal Random Variables 499 A.7 The Law of Averages 500 A.8 Higher Moments and the Moment Generating Function 501 Appendix B Probability Distributions 505 B.1 The Bernoulli and Binomial Distributions 505 B.2 The Multinomial Distribution 506 B.3 The Geometric Distribution 508 B.4 The Negative Binomial Distribution 509 B.5 The Hypergeometric Distribution 510 B.6 The Poisson Distribution 511 B.7 The Uniform Distribution 513 B.8 The Exponential Distribution 513 B.9 The Gamma Distribution 514 B.10 The Chi-Square Distribution 517 B.11 The Student’s t Distribution 520 B.12 The Beta Distribution 522 B.13 The F Distribution 523 Exercises 525 Appendix C Distributions Quick Reference 527 Problem Solutions 531 Bibliography 545 Index 553

About the Author :
Laura M. Chihara, PhD, is Professor of Mathematics at Carleton College with extensive experience teaching mathematical statistics and applied regression analysis. Dr. Chihara has experience with S+ and R from her work at Insightful Corporation (formerly MathSoft) and in statistical consulting. Tim C. Hesterberg, PhD, is a Staff Data Scientist at Instacart. He was previously a data scientist at Google and research scientist at Insightful Corporation, led the development of S+Resample, and wrote the R resample package.