
Mathematical Statistics with Resampling and R
by Chihara, Laura M.; Hesterberg, Tim C.Buy New
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Summary
Author Biography
Table of Contents
Preface | p. xiii |
Data and Case Studies | p. 1 |
Case Study: Flight Delays | p. 1 |
Case Study: Birth Weights of Babies | p. 2 |
Case Study: Verizon Repair Times | p. 3 |
Sampling | p. 3 |
Parameters and Statistics | p. 5 |
Case Study: General Social Survey | p. 5 |
Sample Surveys | p. 6 |
Case Study: Beer and Hot Wings | p. 8 |
Case Study: Black Spruce Seedlings | p. 8 |
Studies | p. 8 |
Exercises | p. 10 |
Exploratory Data Analysis | p. 13 |
Basic Plots | p. 13 |
Numeric Summaries | p. 16 |
Center | p. 17 |
Spread | p. 18 |
Shape | p. 19 |
Boxplots | p. 19 |
Quantiles and Normal Quantile Plots | p. 20 |
Empirical Cumulative Distribution Functions | p. 24 |
Scatter Plots | p. 26 |
Skewness and Kurtosis | p. 28 |
Exercises | p. 30 |
Hypothesis Testing | p. 35 |
Introduction to Hypothesis Testing | p. 35 |
Hypotheses | p. 36 |
Permutation Tests | p. 38 |
Implementation Issues | p. 42 |
One-Sided and Two-Sided Tests | p. 47 |
Other Statistics | p. 48 |
Assumptions | p. 51 |
Contingency Tables | p. 52 |
Permutation Test for Independence | p. 54 |
Chi-Square Reference Distribution | p. 57 |
Chi-Square Test of Independence | p. 58 |
Test of Homogeneity | p. 61 |
Goodness-of-Fit: All Parameters Known | p. 63 |
Goodness-of-Fit: Some Parameters Estimated | p. 66 |
Exercises | p. 68 |
Sampling Distributions | p. 77 |
Sampling Distributions | p. 77 |
Calculating Sampling Distributions | p. 82 |
The Central Limit Theorem | p. 84 |
CLT for Binomial Data | p. 87 |
Continuity Correction for Discrete Random Variables | p. 89 |
Accuracy of the Central Limit Theorem | p. 90 |
CLT for Sampling Without Replacement | p. 91 |
Exercises | p. 92 |
The Bootstrap | p. 99 |
Introduction to the Bootstrap | p. 99 |
The Plug-In Principle | p. 106 |
Estimating the Population Distribution | p. 107 |
How Useful Is the Bootstrap Distribution? | p. 109 |
Bootstrap Percentile Intervals | p. 113 |
Two Sample Bootstrap | p. 114 |
The Two Independent Populations Assumption | p. 119 |
Other Statistics | p. 120 |
Bias | p. 122 |
Monte Carlo Sampling: The "Second Bootstrap Principle" | p. 125 |
Accuracy of Bootstrap Distributions | p. 125 |
Samnle Mean: Large Sample Size | p. 126 |
Sample Mean: Small Sample Size | p. 127 |
Sample Median | p. 127 |
How Many Bootstrap Samples are Needed? | p. 129 |
Exercises | p. 129 |
Estimation | p. 135 |
Maximum Likelihood Estimation | p. 135 |
Maximum Likelihood for Discrete Distributions | p. 136 |
Maximum Likelihood for Continuous Distributions | p. 139 |
Maximum Likelihood for Multiple Parameters | p. 143 |
Method of Moments | p. 146 |
Properties of Estimators | p. 148 |
Unbiasedness | p. 148 |
Efficiency | p. 151 |
Mean Square Error | p. 155 |
Consistency | p. 157 |
Transformation Invariance | p. 160 |
Exercises | p. 161 |
Classical Inference: Confidence Intervals | p. 167 |
Confidence Intervals for Means | p. 167 |
Confidence Intervals for a Mean, $$$ Known | p. 167 |
Confidence Intervals for a Mean, $$$ Unknown | p. 172 |
Confidence Intervals for a Difference in Means | p. 178 |
Confidence Intervals in General | p. 183 |
Location and Scale Parameters | p. 186 |
One-Sided Confidence Intervals | p. 189 |
Confidence Intervals for Proportions | p. 191 |
The Agresti-Coull Interval for a Proportion | p. 193 |
Confidence Interval for the Difference of Proportions | p. 194 |
Bootstrap t Confidence Intervals | p. 195 |
Comparing Bootstrap t and Formula t Confidence Intervals | p. 200 |
Exercises | p. 200 |
Classical Inference: Hypothesis Testing | p. 211 |
Hypothesis Tests for Means and Proportions | p. 211 |
One Population | p. 211 |
Comparing Two Populations | p. 215 |
Type I and Type II Errors | p. 221 |
Type I Errors | p. 221 |
Type II Errors and Power | p. 226 |
More on Testing | p. 231 |
On Significance | p. 231 |
Adjustments for Multiple Testing | p. 232 |
P-values Versus Critical Regions | p. 233 |
Likelihood Ratio Tests | p. 234 |
Simple Hypotheses and the Neyman-Pearson Lemma | p. 234 |
Generalized Likelihood Ratio Tests | p. 237 |
Exercises | p. 239 |
Regression | p. 247 |
Covariance | p. 247 |
Correlation | p. 251 |
Least-Squares Regression | p. 254 |
Regression Toward the Mean | p. 258 |
Variation | p. 259 |
Diagnostics | p. 261 |
Multiple Regression | p. 265 |
The Simple Linear Model | p. 266 |
Inference for ¿ and ß | p. 270 |
Inference for the Response | p. 273 |
Comments About Assumptions for the Linear Model | p. 277 |
Resampling Correlation and Regression | p. 279 |
Permutation Tests | p. 282 |
Bootstrap Case Study: Bushmeat | p. 283 |
Logistic Regression | p. 286 |
Inference for Logistic Regression | p. 291 |
Exercises | p. 294 |
Bayesian Methods | p. 301 |
Bayes' Theorem | p. 302 |
Binomial Data, Discrete Prior Distributions | p. 302 |
Binomial Data, Continuous Prior Distributions | p. 309 |
Continuous Data | p. 316 |
Sequential Data | p. 319 |
Exercises | p. 322 |
Additional Topics | p. 327 |
Smoothed Bootstrap | p. 327 |
Kernel Density Estimate | p. 328 |
Parametric Bootstrap | p. 331 |
The Delta Method | p. 335 |
Stratified Sampling | p. 339 |
Computational Issues in Bayesian Analysis | p. 340 |
Monte Carlo Integration | p. 341 |
Importance Sampling | p. 346 |
Ratio Estimate for Importance Sampling | p. 352 |
Importance Sampling in Bayesian Applications | p. 355 |
Exercises | p. 359 |
Review of Probability | p. 363 |
Basic Probability | p. 363 |
Mean and Variance | p. 364 |
The Mean of a Sample of Random Variables | p. 366 |
The Law of Averages | p. 367 |
The Normal Distribution | p. 368 |
Sums of Normal Random Variables | p. 369 |
Higher Moments and the Moment Generating Function | p. 370 |
Probability Distributions | p. 373 |
The Bernoulli and Binomial Distributions | p. 373 |
The Multinomial Distribution | p. 374 |
The Geometric Distribution | p. 376 |
The Negative Binomial Distribution | p. 377 |
The Hypergeometric Distribution | p. 378 |
The Poisson Distribution | p. 379 |
The Uniform Distribution | p. 381 |
The Exponential Distribution | p. 381 |
The Gamma Distribution | p. 382 |
The Chi-Square Distribution | p. 385 |
The Student's t Distribution | p. 388 |
The Beta Distribution | p. 390 |
The F Distribution | p. 391 |
Exercises | p. 393 |
Distributions Quick Reference | p. 395 |
Solutions to Odd-Numbered Exercises | p. 399 |
Bibliography | p. 407 |
Index | p. 413 |
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