Mathematical Statistics with Resampling and R

Description

Contents......Page 3 Preface......Page 9 Case Study: Flight Delays......Page 12 Case Study: Birth Weights of Babies......Page 13 Case Study: Verizon Repair Times......Page 14 Case Study: Iowa Recidivism......Page 15 Sampling......Page 16 Parameters and Statistics......Page 17 Case Study: General Social Survey......Page 18 Sample Surveys......Page 19 Case Study: Beer and Hot Wings......Page 20 Studies......Page 21 Google Interview Question: Mobile Ads Optimization......Page 23 Exercises......Page 27 Basic Plots......Page 31 Numeric Summaries......Page 35 Boxplots......Page 38 Quantiles and Normal Quantile Plots......Page 39 Empirical Cumulative Distribution Functions......Page 45 Scatter Plots......Page 48 Skewness and Kurtosis......Page 50 Exercises......Page 52 Introduction to Hypothesis Testing......Page 57 Hypotheses......Page 58 Permutation Tests......Page 60 Matched Pairs......Page 78 Exercises......Page 80 Sampling Distributions......Page 84 Calculating Sampling Distributions......Page 89 The Central Limit Theorem......Page 93 Exercises......Page 102 Introduction to the Bootstrap......Page 111 The Plug-in Principle......Page 118 Bootstrap Percentile Intervals......Page 126 Two-Sample Bootstrap......Page 127 Other Statistics......Page 136 Bias......Page 139 Monte Carlo Sampling: The “Second Bootstrap Principle”......Page 142 Accuracy of Bootstrap Distributions......Page 143 How Many Bootstrap Samples Are Needed?......Page 148 Exercises......Page 149 Maximum Likelihood Estimation......Page 157 Method of Moments......Page 169 Properties of Estimators......Page 171 Statistical Practice......Page 186 Exercises......Page 188 Confidence Intervals for Means......Page 195 Confidence Intervals in General......Page 212 One-sided Confidence Intervals......Page 220 Confidence Intervals for Proportions......Page 222 Bootstrap Confidence Intervals......Page 227 Confidence Interval Properties......Page 234 Exercises......Page 236 Hypothesis Tests for Means and Proportions: One Population......Page 248 -Tests......Page 253 Hypothesis Tests for Means and Proportions: Two Populations......Page 255 Type I and Type II Errors......Page 262 Interpreting Test Results......Page 274 Likelihood Ratio Tests......Page 278 Statistical Practice......Page 286 Exercises......Page 292 Covariance......Page 304 Correlation......Page 308 Least-Squares Regression......Page 311 The Simple Linear Model......Page 324 Resampling Correlation and Regression......Page 339 Logistic Regression......Page 347 Exercises......Page 357 Independence in Contingency Tables......Page 366 Permutation Test of Independence......Page 368 Chi-square Test of Independence......Page 372 Chi-square Test of Homogeneity......Page 379 Goodness-of-fit Tests......Page 381 Chi-square and the Likelihood Ratio*......Page 386 Exercises......Page 387 Bayesian Methods......Page 397 Binomial Data: Discrete Prior Distributions......Page 398 Binomial Data: Continuous Prior Distributions......Page 406 Continuous Data......Page 412 Sequential Data......Page 415 Exercises......Page 420 Comparing Three or More Populations......Page 425 Exercises......Page 435 Smoothed Bootstrap......Page 438 Parametric Bootstrap......Page 442 The Delta Method......Page 446 Stratified Sampling......Page 450 Computational Issues in Bayesian Analysis......Page 451 Monte Carlo Integration......Page 453 Importance Sampling......Page 457 The EM Algorithm......Page 472 Exercises......Page 477 A.1 Basic Probability......Page 481 A.2 Mean and Variance......Page 482 A.3 The Normal Distribution......Page 484 A.4 The Mean of a Sample of Random Variables......Page 485 A.5 Sums of Normal Random Variables......Page 486 A.6 TheLawofAverages......Page 487 A.7 Higher Moments and the Moment-generating Function......Page 488 B.1 The Bernoulli and Binomial Distributions......Page 491 B.2 The Multinomial Distribution......Page 492 B.3 The Geometric Distribution......Page 494 B.4 The Negative Binomial Distribution......Page 495 B.5 The Hypergeometric Distribution......Page 496 B.6 The Poisson Distribution......Page 497 B.8 The Exponential Distribution......Page 499 B.9 The Gamma Distribution......Page 501 B.10 The Chi-square Distribution......Page 503 Distribution......Page 506 B.12 The Beta Distribution......Page 508 B.13 The F Distribution......Page 509 Exercises......Page 511 Distributions Quick Reference......Page 513 Solutions for Chapter 2......Page 517 Solutions for Chapter 3......Page 518 Solutions for Chapter 4......Page 519 Solutions for Chapter 6......Page 520 Solutions for Chapter 7......Page 522 Solutions for Chapter 8......Page 523 Solutions for Chapter 9......Page 524 Solutions for Chapter 10......Page 525 Solutions for Chapter 11......Page 526 Solutions for Chapter 13......Page 527 Solutions for Appendix B......Page 528 Refs......Page 529 Index......Page 535