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      1. Naturvetenskap och teknik
      2. Matematik och naturvetenskap
      3. Matematik

      Mathematical Statistics with Resampling and R

      AvLaura M. Chihara,Tim C. Hesterberg

      Inbunden, Engelska, 2022

      1 662 kr

      Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

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      Beskrivning

      Mathematical Statistics with Resampling and R This thoroughly updated third edition combines 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. The third edition of Mathematical Statistics with Resampling and R combines modern resampling techniques and mathematical statistics. This book is classroom-tested to ensure an accessible presentation, and uses the powerful and flexible computer language R for data analysis. This book introduces permutation tests and bootstrap methods to motivate classical inference methods, as well as to be utilized as useful tools in their own right when classical methods are inaccurate or unavailable. The book strikes a balance between simulation, computing, theory, data, and applications. Throughout the book, new and updated case studies representing a diverse range of subjects, such as flight delays, birth weights of babies, U.S. demographics, views on sociological issues, and problems at Google and Instacart, illustrate the relevance of mathematical statistics to real-world applications. Changes and additions to the third edition include: New and updated case studies that incorporate contemporary subjects like COVID-19Several new sections, including introductory material on causal models and regression methods for causal modeling in practiceModern terminology distinguishing statistical discernibility and practical importanceNew exercises and examples, data sets, and R code, using dplyr and ggplot2A complete instructor’s solutions manualA new github site that contains code, data sets, additional topics, and instructor resourcesMathematical Statistics with Resampling and R is an ideal textbook for undergraduate and graduate students in mathematical statistics courses, as well as practitioners and researchers looking to expand their toolkit of resampling and classical techniques.

      Produktinformation

      • Utgivningsdatum:2022-10-24
      • Mått:158 x 234 x 25 mm
      • Vikt:0 g
      • Format:Inbunden
      • Språk:Engelska
      • Antal sidor:576
      • Upplaga:3
      • Förlag:John Wiley & Sons Inc
      • ISBN:9781119874034

      Utforska kategorier

      • Matematik inom Naturvetenskap och teknik

      Mer om författaren

      Laura M. Chihara, PhD, is Professor of Mathematics at Carleton College with extensive experience teaching mathematical statistics and applied regression analysis. Dr. Chihara has experience with S+ and R from her work at Insightful Corporation (formerly MathSoft) and in statistical consulting.Tim C. Hesterberg, PhD, is a Staff Data Scientist at Instacart. He was previously a data scientist at Google and research scientist at Insightful Corporation, led the development of S+Resample, and wrote the R resample package.

      Innehållsförteckning

      • Preface xiii1 Data and Case Studies 11.1 Case Study: Flight Delays 11.2 Case Study: Birth Weights of Babies 21.3 Case Study: Verizon Repair Times 31.4 Case Study: Iowa Recidivism 41.5 Sampling 51.6 Parameters and Statistics 61.7 Case Study: General Social Survey 71.8 Sample Surveys 81.9 Case Study: Beer and Hot Wings 91.10 Case Study: Black Spruce Seedlings 101.11 Studies 111.12 Google Interview Question: Mobile Ads Optimization 13Exercises 162 Exploratory Data Analysis 212.1 Basic Plots 212.2 Numeric Summaries 252.2.1 Center 252.2.2 Spread 262.2.3 Shape 262.3 Boxplots 272.4 Quantiles and Normal Quantile Plots 292.5 Empirical Cumulative Distribution Functions 342.6 Scatter Plots 362.7 Skewness and Kurtosis 38Exercises 393 Introduction to Hypothesis Testing: Permutation Tests 453.1 Introduction to Hypothesis Testing 453.2 Hypotheses 463.3 Permutation Tests 503.3.1 Implementation Issues 543.3.2 One-Sided and Two-Sided Tests 583.3.3 Other Statistics 593.3.4 Conditions 623.3.5 Remark on Terminology 653.4 Matched Pairs 663.5 Cause and Effect 67Exercises 714 Sampling Distributions 774.1 Sampling Distributions 774.2 Calculating Sampling Distributions 824.3 The Central Limit Theorem 854.3.1 CLT for Binomial Data 884.3.2 Continuity Correction for Discrete Random Variables 904.3.3 Accuracy of the Central Limit Theorem* 924.3.4 CLT for Sampling Without Replacement 93Exercises 935 Introduction to Confidence Intervals: The Bootstrap 1035.1 Introduction to the Bootstrap 1035.2 The Plug-in Principle 1095.2.1 Estimating the Population Distribution 1105.2.2 How Useful Is the Bootstrap Distribution? 1125.3 Bootstrap Percentile Intervals 1155.4 Two Sample Bootstrap 1165.4.1 Matched Pairs 1225.5 Other Statistics 1235.6 Bias 1265.7 Monte Carlo Sampling 1305.8 Accuracy of Bootstrap Distributions 1315.8.1 Sample Mean, Large Sample Size 1315.8.2 Sample Mean: Small Sample Size 1325.8.3 Sample Median 1345.8.4 Mean–Variance Relationship 1355.9 How Many Bootstrap Samples Are Needed? 136Exercises 1376 Estimation 1476.1 Maximum Likelihood Estimation 1476.1.1 Maximum Likelihood for Discrete Distributions 1486.1.2 Maximum Likelihood for Continuous Distributions 1506.1.3 Maximum Likelihood for Multiple Parameters 1556.2 Method of Moments 1586.3 Properties of Estimators 1606.3.1 Unbiasedness 1616.3.2 Efficiency 1646.3.3 Mean Square Error 1676.3.4 Consistency 1696.3.5 Transformation Invariance* 1716.3.6 Asymptotic Normality of MLE* 1736.4 Statistical Practice 1746.4.1 Are You Asking the Right Question? 1756.4.2 Weights 175Exercises 1767 More Confidence Intervals 1837.1 Confidence Intervals for Means 1837.1.1 Confidence Intervals for a Mean, Variance Known 1837.1.2 Confidence Intervals for a Mean, Variance Unknown 1887.1.3 Confidence Intervals for a Difference in Means 1957.1.4 Matched Pairs, Revisited 2017.2 Confidence Intervals Using Pivots 2017.2.1 Location and Scale Parameters* 2057.3 One-Sided Confidence Intervals 2097.4 Confidence Intervals for Proportions 2117.4.1 Agresti–Coull Intervals for a Proportion 2147.4.2 Confidence Interval for a Difference of Proportions 2157.5 Bootstrap Confidence Intervals 2167.5.1 T Confidence Intervals Using Bootstrap Standard Errors 2167.5.2 Bootstrap t Confidence Intervals 2177.5.3 Comparing Bootstrap t and Formula t Confidence Intervals 2237.6 Confidence Interval Properties 2247.6.1 Confidence Interval Accuracy 2247.6.2 Confidence Interval Length 2257.6.3 Transformation Invariance 2257.6.4 Ease of Use and Interpretation 2257.6.5 Research Needed 2267.7 The Delta Method* 226Exercises 2308 More Hypothesis Testing 2458.1 Hypothesis Tests for Means and Proportions: One Population 2458.1.1 A Single Mean 2458.1.2 One Proportion 2488.2 Bootstrap t Tests 2508.3 Hypothesis Tests for Means and Proportions: Two Populations 2528.3.1 Comparing Two Means 2528.3.2 Comparing Two Proportions 2558.3.3 Matched Pairs for Proportions 2598.4 Type I and Type II Errors 2618.4.1 Type I Errors 2628.4.2 Type II Errors and Power 2678.4.3 P-Values Versus Critical Regions 2728.4.4 Relationship Between Confidence Intervals and Hypothesis Tests 2738.5 Interpreting Test Results 2768.5.1 Terminology 2778.5.2 Arbitrary Thresholds 2778.5.3 Statistical Discernibility Versus Practical Importance 2778.5.4 Negative Results 2788.5.5 Inflated False Positive Rate 2798.6 Likelihood Ratio Tests 2818.6.1 Simple Hypotheses and the Neyman–Pearson Lemma 2818.6.2 Likelihood Ratio Tests for Composite Hypotheses 2858.7 Statistical Practice 2898.7.1 More Campaigns with No Clicks and No Conversions 293Exercises 2949 Regression 3099.1 Covariance 3099.2 Correlation 3139.3 Least Squares Regression 3169.3.1 Regression toward the Mean 3209.3.2 Variation 3219.3.3 Diagnostics 3239.3.4 Multiple Regression 3289.4 The Simple Linear Model 3299.4.1 Inference for α and β 3339.4.2 Inference for the Response 3369.4.3 Comments About Conditions for the Linear Model 3409.5 Resampling Correlation and Regression 3429.5.1 Permutation Tests 3459.5.2 Bootstrap Case Study: Bushmeat 3469.6 Logistic Regression 3509.6.1 Inference for Logistic Regression 355Exercises 35710 Categorical Data 36710.1 Independence in Contingency Tables 36710.2 Permutation Test of Independence 36910.3 Chi-Square Test of Independence 37110.3.1 Model for Chi-Square Test of Independence 37310.3.2 2 × 2Tables 37610.3.3 Fisher’s Exact Test 37810.3.4 Conditioning 37910.4 Chi-Square Test of Homogeneity 38010.5 Goodness-of-Fit Tests 38210.5.1 All Parameters Known 38210.5.2 Some Parameters Estimated 38510.6 Chi-Square and the Likelihood Ratio* 388Exercises 38911 Bayesian Methods 39911.1 Bayes Theorem 40011.2 Binomial Data: Discrete Prior Distributions 40011.3 Binomial Data: Continuous Prior Distributions 40811.4 Continuous Data 41411.5 Sequential Data 417Exercises 42112 One-Way ANOVA 42912.1 Comparing Three or More Populations 42912.1.1 The ANOVA F Test 42912.1.2 A Permutation Test Approach 438Exercises 43913 Additional Topics 44313.1 Smoothed Bootstrap 44413.1.1 Kernel Density Estimate 44413.2 Parametric Bootstrap 44913.3 Stratified Sampling 45213.3.1 Post-stratification 45313.3.2 Optimal Stratified Sampling 45413.4 Control Variates and Casual Modeling 45513.4.1 Control Variates in Experiments 45713.4.2 Potential Outcomes Framework 46013.4.3 Observational Data – Causal Modeling 46113.5 Computational Issues in Bayesian Analysis 46213.6 Monte Carlo Integration 46413.7 Importance Sampling 46813.7.1 Ratio Estimate for Importance Sampling 47513.7.2 Importance Sampling in Bayesian Applications 47813.8 The EM Algorithm 48313.8.1 EM in General 485Exercises 488Appendix A Review of Probability 493A.1 Basic Probability 493A.2 Mean and Variance 494A.3 Marginal and Conditional Distributions 496A.4 The Normal Distribution 497A.5 The Mean of a Sample of Random Variables 498A.6 Sums of Normal Random Variables 499A.7 The Law of Averages 500A.8 Higher Moments and the Moment Generating Function 501Appendix B Probability Distributions 505B. 1 The Bernoulli and Binomial Distributions 505B. 2 The Multinomial Distribution 506B. 3 The Geometric Distribution 508B. 4 The Negative Binomial Distribution 509B. 5 The Hypergeometric Distribution 510B. 6 The Poisson Distribution 511B. 7 The Uniform Distribution 513B. 8 The Exponential Distribution 513B. 9 The Gamma Distribution 514B. 10 The Chi-Square Distribution 517B. 11 The Student’s t Distribution 520B. 12 The Beta Distribution 522B. 13 The F Distribution 523Exercises 525Appendix C Distributions Quick Reference 527Problem Solutions 531Bibliography 545Index 553
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