Mathematical statistics : with resampling and R
This book bridges the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply mod...
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Hoboken
Wiley
2011
John Wiley & Sons, Incorporated Wiley-Blackwell |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9781118029855 1118029852 |
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| Abstract | This book bridges the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques. The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as: Exploratory data analysis Calculation of sampling distributions The Central Limit Theorem Monte Carlo sampling Maximum likelihood estimation and properties of estimators Confidence intervals and hypothesis tests Regression Bayesian methods Throughout the book, case studies on diverse subjects such as flight delays, birth weights of babies, and telephone company repair times illustrate the relevance of the real-world applications of the discussed material. Key definitions and theorems of important probability distributions are collected at the end of the book, and a related website is also available, featuring additional material including data sets, R scripts, and helpful teaching hints. Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work. |
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| AbstractList | This book bridges the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques. The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as: Exploratory data analysis Calculation of sampling distributions The Central Limit Theorem Monte Carlo sampling Maximum likelihood estimation and properties of estimators Confidence intervals and hypothesis tests Regression Bayesian methods Throughout the book, case studies on diverse subjects such as flight delays, birth weights of babies, and telephone company repair times illustrate the relevance of the real-world applications of the discussed material. Key definitions and theorems of important probability distributions are collected at the end of the book, and a related website is also available, featuring additional material including data sets, R scripts, and helpful teaching hints. Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work. This book bridges the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques. The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as: Exploratory data analysis Calculation of sampling distributions The Central Limit Theorem Monte Carlo sampling Maximum likelihood estimation and properties of estimators Confidence intervals and hypothesis tests Regression Bayesian methods Throughout the book, case studies on diverse subjects such as flight delays, birth weights of babies, and telephone company repair times illustrate the relevance of the real-world applications of the discussed material. Key definitions and theorems of important probability distributions are collected at the end of the book, and a related website is also available, featuring additional material including data sets, R scripts, and helpful teaching hints. Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work. This book bridges the latest software applications with the benefits of modern resampling techniquesResampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques.The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as:Exploratory data analysisCalculation of sampling distributionsThe Central Limit TheoremMonte Carlo samplingMaximum likelihood estimation and properties of estimatorsConfidence intervals and hypothesis testsRegressionBayesian methodsThroughout the book, case studies on diverse subjects such as flight delays, birth weights of babies, and telephone company repair times illustrate the relevance of the real-world applications of the discussed material. Key definitions and theorems of important probability distributions are collected at the end of the book, and a related website is also available, featuring additional material including data sets, R scripts, and helpful teaching hints.Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work. |
| Author | Chihara, Laura Hesterberg, Tim |
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| Notes | Includes bibliographical references (p. 407-412) and index |
| OCLC | 815388976 1347027877 |
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| PublicationPlace | Hoboken |
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| Publisher | Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
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| Snippet | This book bridges the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of... This book bridges the latest software applications with the benefits of modern resampling techniquesResampling helps students understand the meaning of... |
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| SubjectTerms | Mathematics Resampling (Statistics) Statistics |
| TableOfContents | 8.4.2 Generalized Likelihood Ratio Tests -- 8.5 Exercises -- 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 ß -- 9.4.2 Inference for the Response -- 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 -- 9.7 Exercises -- 10: Bayesian Methods -- 10.1 Bayes' Theorem -- 10.2 Binomial Data, Discrete Prior Distributions -- 10.3 Binomial Data, Continuous Prior Distributions -- 10.4 Continuous Data -- 10.5 Sequential Data -- 10.6 Exercises -- 11: Additional Topics -- 11.1 Smoothed Bootstrap -- 11.1.1 Kernel Density Estimate -- 11.2 Parametric Bootstrap -- 11.3 The Delta Method -- 11.4 Stratified Sampling -- 11.5 Computational Issues in Bayesian Analysis -- 11.6 Monte Carlo Integration -- 11.7 Importance Sampling -- 11.7.1 Ratio Estimate for Importance Sampling -- 11.7.2 Importance Sampling in Bayesian Applications -- 11.8 Exercises -- Appendix A: Review of Probability -- A.1 Basic Probability -- A.2 Mean and Variance -- A.3 The Mean of a Sample of Random Variables -- A.4 The Law of Averages -- A.5 The Normal Distribution -- A.6 Sums of Normal Random Variables -- A.7 Higher Moments and the Moment Generating Function -- Appendix 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 Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- 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 Sampling -- 1.5 Parameters and Statistics -- 1.6 Case Study: General Social Survey -- 1.7 Sample Surveys -- 1.8 Case Study: Beer and Hot Wings -- 1.9 Case Study: Black Spruce Seedlings -- 1.10 Studies -- 1.11 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 -- 2.8 Exercises -- 3: Hypothesis Testing -- 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 -- 3.4 Contingency Tables -- 3.4.1 Permutation Test for Independence -- 3.4.2 Chi-square Reference Distribution -- 3.5 Chi-square Test of Independence -- 3.6 Test of Homogeneity -- 3.7 Goodness-of-fit: All Parameters Known -- 3.8 Goodness-of-fit: Some Parameters Estimated -- 3.9 Exercises -- 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 Samplingwithout Replacement -- 4.4 Exercises -- 5: 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 The Two Independent Populations Assumption -- 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 -- 5.9 How Many Bootstrap Samples Are Needed? -- 5.10 Exercises -- 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 -- 6.4 Exercises -- 7: Classical Inference: Confidence Intervals -- 7.1 Confidence Intervals for Means -- 7.1.1 Confidence Intervals for a Mean, σ Known -- 7.1.2 Confidence Intervals for a Mean, σ Unknown -- 7.1.3 Confidence Intervals for a Difference in Means -- 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 t Confidence Intervals -- 7.5.1 Comparing Bootstrap t and Formula t Confidence Intervals -- 7.6 Exercises -- 8: Classical Inference: Hypothesis Testing -- 8.1 Hypothesis Tests for Means and Proportions -- 8.1.1 One Population -- 8.1.2 Comparing Two Populations -- 8.2 Type I and Type Ii Errors -- 8.2.1 Type I Errors -- 8.2.2 Type II Errors and Power -- 8.3 More on Testing -- 8.3.1 on Significance -- 8.3.2 Adjustments for Multiple Testing -- 8.3.3 P-values Versus Critical Regions -- 8.4 Likelihood Ratio Tests -- 8.4.1 Simple Hypotheses and the Neyman-pearson Lemma B.10 The Chi-square Distribution -- B.11 The Student's t Distribution -- B.12 The Beta Distribution -- B.13 The f Distribution -- B.14 Exercises -- Appendix C: Distributions Quick Reference -- Solutions to Odd-numbered Exercises -- Bibliography -- Index 7.4 Confidence Intervals for Proportions -- 7.5 Bootstrap t Confidence Intervals -- 7.6 Exercises -- Chapter 8: Classical Inference: Hypothesis Testing -- 8.1 Hypothesis Tests for Means and Proportions -- 8.2 Type I and Type Ii Errors -- 8.3 More on Testing -- 8.4 Likelihood Ratio Tests -- 8.5 Exercises -- Chapter 9: Regression -- 9.1 Covariance -- 9.2 Correlation -- 9.3 Least-Squares Regression -- 9.4 The Simple Linear Model -- 9.5 Resampling Correlation and Regression -- 9.6 Logistic Regression -- 9.7 Exercises -- Chapter 10: Bayesian Methods -- 10.1 Bayes'Theorem -- 10.2 Binomial Data, Discrete Prior Distributions -- 10.3 Binomial Data, Continuous Prior Distributions -- 10.4 Continuous Data -- 10.5 Sequential Data -- 10.6 Exercises -- Chapter 11: Additional Topics -- 11.1 Smoothed Bootstrap -- 11.2 Parametric Bootstrap -- 11.3 The Delta Method -- 11.4 Stratified Sampling -- 11.5 Computational Issues in Bayesian Analysis -- 11.6 Monte Carlo Integration -- 11.7 Importance Sampling -- 11.8 Exercises -- Appendix A: Review of Probability -- A.1 Basic Probability -- A.2 Mean and Variance -- A.3 The Mean of A Sample of Random Variables -- A.4 The Law of Averages -- A.5 The Normal Distribution -- A.6 Sums of Normal Random Variables -- A.7 Higher Moments and the Moment Generating Function -- Appendix 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 -- B.14 Exercises -- Appendix C: Distributions Quick Reference Intro -- Half Title page -- Title page -- Copyright page -- Preface -- Acknowledgments -- 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 Sampling -- 1.5 Parameters and Statistics -- 1.6 Case Study: General Social Survey -- 1.7 Sample Surveys -- 1.8 Case Study: Beer and Hot Wings -- 1.9 Case Study: Black Spruce Seedlings -- 1.10 Studies -- 1.11 Exercises -- Chapter 2: Exploratory Data Analysis -- 2.1 Basic Plots -- 2.2 Numeric Summaries -- 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 -- 2.8 Exercises -- Chapter 3: Hypothesis Testing -- 3.1 Introduction to Hypothesis Testing -- 3.2 Hypotheses -- 3.3 Permutation Tests -- 3.4 Contingency Tables -- 3.5 Chi-Square Test of Independence -- 3.6 Test of Homogeneity -- 3.7 Goodness-of-Fit: All Parameters Known -- 3.8 Goodness-of-Fit: Some Parameters Estimated -- 3.9 Exercises -- Chapter 4: Sampling Distributions -- 4.1 Sampling Distributions -- 4.2 Calculating Sampling Distributions -- 4.3 The Central Limit Theorem -- 4.4 Exercises -- Chapter 5: The Bootstrap -- 5.1 Introduction to the Bootstrap -- 5.2 The Plug-in Principle -- 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 -- 5.9 How Many Bootstrap Samples are Needed? -- 5.10 Exercises -- Chapter 6: Estimation -- 6.1 Maximum Likelihood Estimation -- 6.2 Method of Moments -- 6.3 Properties of Estimators -- 6.4 Exercises -- Chapter 7: Classical Inference: Confidence Intervals -- 7.1 Confidence Intervals for Means -- 7.2 Confidence Intervals in General -- 7.3 One-Sided Confidence Intervals Solutions to Odd-Numbered Exercises -- Bibliography -- Index |
| Title | Mathematical statistics : with resampling and R |
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