内容

目次

Dedication Preface 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 Exercises 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 Exercises 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 Exercises 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 Exercises 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? Exercises 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 Exercises 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 Exercises 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 Exercises 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 Exercises 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∗ Exercises 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 Exercises 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 Exercises 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 Exercises 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 Exercises C Distributions Quick Reference Problem Solutions Bibliography Index