Mathematical Statistics with Resampling and R

Cover
Title Page
Copyright
Contents
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
Chapter 2 Exploratory Data Analysis
	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
		3.3.3 Other Statistics
		3.3.4 Conditions
		3.3.5 Remark on Terminology
	3.4 Matched Pairs
	3.5 Cause and Effect
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
		5.4.1 Matched Pairs
	5.5 Other Statistics
	5.6 Bias
	5.7 Monte Carlo Sampling
	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
		6.4.1 Are You Asking the Right Question?
		6.4.2 Weights
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
			7.1.2.1 Check Conditions
			7.1.2.2 Nonnormal Populations
		7.1.3 Confidence Intervals for a Difference in Means
			7.1.3.1 Check Conditions
			7.1.3.2 Nonnormal Populations, Revisited
			7.1.3.3 Pooling the Variances*
		7.1.4 Matched Pairs, Revisited
	7.2 Confidence Intervals Using Pivots
		7.2.1 Location and Scale Parameters*
	7.3 One‐Sided Confidence Intervals
	7.4 Confidence Intervals for Proportions
		7.4.1 Agresti–Coull Intervals for a Proportion
		7.4.2 Confidence Interval for a Difference of Proportions
	7.5 Bootstrap Confidence Intervals
		7.5.1 T Confidence Intervals Using Bootstrap Standard Errors
		7.5.2 Bootstrap t Confidence Intervals
			7.5.2.1 Bootstrap t Confidence Intervals for Difference of Means
			7.5.2.2 Bootstrap t Confidence Intervals for Other Statistics
		7.5.3 Comparing Bootstrap t and Formula t Confidence Intervals
	7.6 Confidence Interval Properties
		7.6.1 Confidence Interval Accuracy
		7.6.2 Confidence Interval Length
		7.6.3 Transformation Invariance
		7.6.4 Ease of Use and Interpretation
		7.6.5 Research Needed
	7.7 The Delta Method*
Chapter 8 More Hypothesis Testing
	8.1 Hypothesis Tests for Means and Proportions: One Population
		8.1.1 A Single Mean
			8.1.1.1 Check Conditions
		8.1.2 One Proportion
			8.1.2.1 Normal Approximation with Continuity Correction
	8.2 Bootstrap t Tests
	8.3 Hypothesis Tests for Means and Proportions: Two Populations
		8.3.1 Comparing Two Means
			8.3.1.1 Check Conditions
			8.3.1.2 Matched Pairs
			8.3.1.3 Pooling the Variances*
		8.3.2 Comparing Two Proportions
			8.3.2.1 Monetary Incentives in Surveys, Cont.
		8.3.3 Matched Pairs for 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
		8.4.4 Relationship Between Confidence Intervals and Hypothesis Tests
	8.5 Interpreting Test Results
		8.5.1 Terminology
		8.5.2 Arbitrary Thresholds
		8.5.3 Statistical Discernibility Versus Practical Importance
		8.5.4 Negative Results
		8.5.5 Inflated False Positive Rate
			8.5.5.1 Data Snooping
			8.5.5.2 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
		8.7.1 More Campaigns with No Clicks and No Conversions
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 Conditions for the Linear Model
			9.4.3.1 The x Values Are Fixed
			9.4.3.2 The Relationship Between the Variables Is Linear
			9.4.3.3 The Residuals Are Independent
			9.4.3.4 The Residuals Have Constant Variance
			9.4.3.5 The Residuals Are Normally Distributed
	9.5 Resampling Correlation and Regression
		9.5.1 Permutation Tests
		9.5.2 Bootstrap Case Study: Bushmeat
	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 2×2 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
			12.1.1.1 Conditions
		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 Stratified Sampling
		13.3.1 Post‐stratification
		13.3.2 Optimal Stratified Sampling
	13.4 Control Variates and Casual Modeling
		13.4.1 Control Variates in Experiments
		13.4.2 Potential Outcomes Framework
		13.4.3 Observational Data – Causal Modeling
	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 EM in General
A Review of Probability
	A.1 Basic Probability
	A.2 Mean and Variance
	A.3 Marginal and Conditional Distributions
	A.4 The Normal Distribution
	A.5 The Mean of a Sample of Random Variables
	A.6 Sums of Normal Random Variables
	A.7 The Law of Averages
	A.8 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
Bibliography
Index
EULA