Mathematical statistics with resampling and R / Laura Chihara, Tim Hesterberg.

Includes bibliographical references and index.

Machine generated contents note: 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
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
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
Contents note continued: 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
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
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: The "Second Bootstrap Principle"
5.8.Accuracy of Bootstrap Distributions
Contents note continued: 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?
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
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
Contents note continued: 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.Agresti
Coull Intervals for a Proportion
7.4.2.Confidence Intervals 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
7.5.3.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
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
Contents note continued: 8.3.Hypothesis Tests for Means and Proportions: Two Populations
8.3.1.Comparing Two Means
8.3.2.Comparing Two Proportions
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
8.5.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
8.7.1.More Campaigns with No Clicks and No Conversions
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.A Multiple Regression
9.4.The Simple Linear Model
9.4.1.Inference for α and β
9.4.2.Inference for the Response
Contents note continued: 9.4.3.Comments About Assumptions for the Linear Model
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
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 [&​#x00D7;] 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*
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
12.One-way ANOVA
Contents note continued: 12.1.Comparing Three or More Populations
12.1.1.The ANOVA F-test
12.1.2.A Permutation Test Approach
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
Appendix 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
Appendix B Probability Distributions
B.1.The Bernoulli and Binomial Distributions
Contents note continued: 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
Appendix C Distributions Quick Reference.