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Mathematical Statistics with Resampling and R
Mathematical Statistics with Resampling and R
Autore Chihara Laura M
Edizione [1st ed.]
Pubbl/distr/stampa Somerset : , : John Wiley & Sons, Incorporated, , 2011
Descrizione fisica 1 online resource (434 pages)
Disciplina 310
Altri autori (Persone) HesterbergTim C
Soggetto topico Mathematics
Resampling (Statistics)
Statistics
Soggetto genere / forma Electronic books.
ISBN 9781118518953
9781118029855
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
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.
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.
Record Nr. UNINA-9910795981403321
Chihara Laura M  
Somerset : , : John Wiley & Sons, Incorporated, , 2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Mathematical Statistics with Resampling and R
Mathematical Statistics with Resampling and R
Autore Chihara Laura M
Edizione [1st ed.]
Pubbl/distr/stampa Somerset : , : John Wiley & Sons, Incorporated, , 2011
Descrizione fisica 1 online resource (434 pages)
Disciplina 310
Altri autori (Persone) HesterbergTim C
Soggetto topico Mathematics
Resampling (Statistics)
Statistics
ISBN 9781118518953
9781118029855
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 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.
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.
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.
Record Nr. UNINA-9910809142703321
Chihara Laura M  
Somerset : , : John Wiley & Sons, Incorporated, , 2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui