Course in Statistics with R
Integrates the theory and applications of statistics using R this book has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during ea...
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| Main Authors | , , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Chichester
John Wiley & Sons
2016
Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9781119152729 1119152720 9781119152750 1119152755 |
| DOI | 10.1002/9781119152743 |
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| Abstract | Integrates the theory and applications of statistics using R this book has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. |
|---|---|
| AbstractList | Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models. Key features: Integrates R basics with statistical concepts Provides graphical presentations inclusive of mathematical expressions Aids understanding of limit theorems of probability with and without the simulation approach Presents detailed algorithmic development of statistical models from scratch Includes practical applications with over 50 data sets Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. Linear regression models, experimental designs, multivariate analysis, and categorical data analysis are treated in a way which makes effective use of visualization techniques and the related statistical techniques underlying them through practical applications, and hence helps the reader to achieve a clear understanding of the associated statistical models. Key features: Integrates R basics with statistical conceptsProvides graphical presentations inclusive of mathematical expressionsAids understanding of limit theorems of probability with and without the simulation approachPresents detailed algorithmic development of statistical models from scratchIncludes practical applications with over 50 data sets Integrates the theory and applications of statistics using R this book has been written to bridge the gap between theory and applications and explain how mathematical expressions are converted into R programs. The book has been primarily designed as a useful companion for a Masters student during each semester of the course, but will also help applied statisticians in revisiting the underpinnings of the subject. With this dual goal in mind, the book begins with R basics and quickly covers visualization and exploratory analysis. Probability and statistical inference, inclusive of classical, nonparametric, and Bayesian schools, is developed with definitions, motivations, mathematical expression and R programs in a way which will help the reader to understand the mathematical development as well as R implementation. |
| Author | Tattar Prabhanjan Narayanachar Manjunath B. G Ramaiah Suresh |
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| Notes | Includes bibliographical references (p. [633]-642) and indexes |
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| Snippet | Integrates the theory and applications of statistics using R this book has been written to bridge the gap between theory and applications and explain how... Integrates the theory and applications of statistics using R A Course in Statistics with R has been written to bridge the gap between theory and applications... |
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| SubjectTerms | COMPUTERS Data processing General Engineering & Project Administration General References Mathematical statistics Mathematical statistics -- Data processing R (Computer program language) |
| TableOfContents | Title Page
List of Figures
List of Tables
Preface
Table of Contents
1. Why R?
2. The R Basics
3. Data Preparation and other Tricks
4. Exploratory Data Analysis
5. Probability Theory
6. Probability and Sampling Distributions
7. Parametric Inference
8. Nonparametric Inference
9. Bayesian Inference
10. Stochastic Processes
11. Monte Carlo Computations
12. Linear Regression Models
13. Experimental Designs
14. Multivariate Statistical Analysis - I
15. Multivariate Statistical Analysis - II
16. Categorical Data Analysis
17. Generalized Linear Models
Appendices
Bibliography
Author Index
Subject Index
R Codes 4.1 Introduction: The Tukey's School of Statistics -- 4.2 Essential Summaries of EDA -- 4.3 Graphical Techniques in EDA -- 4.3.1 Boxplot -- 4.3.2 Histogram -- 4.3.3 Histogram Extensions and the Rootogram -- 4.3.4 Pareto Chart -- 4.3.5 Stem-and-Leaf Plot -- 4.3.6 Run Chart -- 4.3.7 Scatter Plot -- 4.4 Quantitative Techniques in EDA -- 4.4.1 Trimean -- 4.4.2 Letter Values -- 4.5 Exploratory Regression Models -- 4.5.1 Resistant Line -- 4.5.2 Median Polish -- 4.6 Further Reading -- 4.7 Complements, Problems, and Programs -- Part II Probability and Inference -- Chapter 5 Probability Theory -- 5.1 Introduction -- 5.2 Sample Space, Set Algebra, and Elementary Probability -- 5.3 Counting Methods -- 5.3.1 Sampling: The Diverse Ways -- 5.3.2 The Binomial Coefficients and the Pascals Triangle -- 5.3.3 Some Problems Based on Combinatorics -- 5.4 Probability: A Definition -- 5.4.1 The Prerequisites -- 5.4.2 The Kolmogorov Definition -- 5.5 Conditional Probability and Independence -- 5.6 Bayes Formula -- 5.7 Random Variables, Expectations, and Moments -- 5.7.1 The Definition -- 5.7.2 Expectation of Random Variables -- 5.8 Distribution Function, Characteristic Function, and Moment Generation Function -- 5.9 Inequalities -- 5.9.1 The Markov Inequality -- 5.9.2 The Jensen's Inequality -- 5.9.3 The Chebyshev Inequality -- 5.10 Convergence of Random Variables -- 5.10.1 Convergence in Distributions -- 5.10.2 Convergence in Probability -- 5.10.3 Convergence in rth Mean -- 5.10.4 Almost Sure Convergence -- 5.11 The Law of Large Numbers -- 5.11.1 The Weak Law of Large Numbers -- 5.12 The Central Limit Theorem -- 5.12.1 The de Moivre-Laplace Central Limit Theorem -- 5.12.2 CLT for iid Case -- 5.12.3 The Lindeberg-Feller CLT -- 5.12.4 The Liapounov CLT -- 5.13 Further Reading -- 5.13.1 Intuitive, Elementary, and First Course Source 5.13.2 The Classics and Second Course Source -- 5.13.3 The Problem Books -- 5.13.4 Other Useful Sources -- 5.13.5 R for Probability -- 5.14 Complements, Problems, and Programs -- Chapter 6 Probability and Sampling Distributions -- 6.1 Introduction -- 6.2 Discrete Univariate Distributions -- 6.2.1 The Discrete Uniform Distribution -- 6.2.2 The Binomial Distribution -- 6.2.3 The Geometric Distribution -- 6.2.4 The Negative Binomial Distribution -- 6.2.5 Poisson Distribution -- 6.2.6 The Hypergeometric Distribution -- 6.3 Continuous Univariate Distributions -- 6.3.1 The Uniform Distribution -- 6.3.2 The Beta Distribution -- 6.3.3 The Exponential Distribution -- 6.3.4 The Gamma Distribution -- 6.3.5 The Normal Distribution -- 6.3.6 The Cauchy Distribution -- 6.3.7 The t-Distribution -- 6.3.8 The Chi-square Distribution -- 6.3.9 The F-Distribution -- 6.4 Multivariate Probability Distributions -- 6.4.1 The Multinomial Distribution -- 6.4.2 Dirichlet Distribution -- 6.4.3 The Multivariate Normal Distribution -- 6.4.4 The Multivariate t Distribution -- 6.5 Populations and Samples -- 6.6 Sampling from the Normal Distributions -- 6.7 Some Finer Aspects of Sampling Distributions -- 6.7.1 Sampling Distribution of Median -- 6.7.2 Sampling Distribution of Mean of Standard Distributions -- 6.8 Multivariate Sampling Distributions -- 6.8.1 Noncentral Univariate Chi-square, t, and F Distributions -- 6.8.2 Wishart Distribution -- 6.8.3 Hotellings T2 Distribution -- 6.9 Bayesian Sampling Distributions -- 6.10 Further Reading -- 6.11 Complements, Problems, and Programs -- Chapter 7 Parametric Inference -- 7.1 Introduction -- 7.2 Families of Distribution -- 7.2.1 The Exponential Family -- 7.2.2 Pitman Family -- 7.3 Loss Functions -- 7.4 Data Reduction -- 7.4.1 Sufficiency -- 7.4.2 Minimal Sufficiency -- 7.5 Likelihood and Information -- 7.5.1 The Likelihood Principle Cover -- Title Page -- Copyright -- Dedication -- Contents -- List of Figures -- List of Tables -- Preface -- Acknowledgments -- Part I The Preliminaries -- Chapter 1 Why R? -- 1.1 Why R? -- 1.2 R Installation -- 1.3 There is Nothing such as PRACTICALS -- 1.4 Datasets in R and Internet -- 1.4.1 List of Web-sites containing DATASETS -- 1.4.2 Antique Datasets -- 1.5 http://cran.r-project.org -- 1.5.1 http://r-project.org -- 1.5.2 http://www.cran.r-project.org/web/views/ -- 1.5.3 Is subscribing to R-Mailing List useful? -- 1.6 R and its Interface with other Software -- 1.7 help and/or? -- 1.8 R Books -- 1.9 A Road Map -- Chapter 2 The R Basics -- 2.1 Introduction -- 2.2 Simple Arithmetics and a Little Beyond -- 2.2.1 Absolute Values, Remainders, etc. -- 2.2.2 round, floor, etc. -- 2.2.3 Summary Functions -- 2.2.4 Trigonometric Functions -- 2.2.5 Complex Numbers -- 2.2.6 Special Mathematical Functions -- 2.3 Some Basic R Functions -- 2.3.1 Summary Statistics -- 2.3.2 is, as, is.na, etc. -- 2.3.3 factors, levels, etc. -- 2.3.4 Control Programming -- 2.3.5 Other Useful Functions -- 2.3.6 Calculus* -- 2.4 Vectors and Matrices in R -- 2.4.1 Vectors -- 2.4.2 Matrices -- 2.5 Data Entering and Reading from Files -- 2.5.1 Data Entering -- 2.5.2 Reading Data from External Files -- 2.6 Working with Packages -- 2.7 R Session Management -- 2.8 Further Reading -- 2.9 Complements, Problems, and Programs -- Chapter 3 Data Preparation and Other Tricks -- 3.1 Introduction -- 3.2 Manipulation with Complex Format Files -- 3.3 Reading Datasets of Foreign Formats -- 3.4 Displaying R Objects -- 3.5 Manipulation Using R Functions -- 3.6 Working with Time and Date -- 3.7 Text Manipulations -- 3.8 Scripts and Text Editors for R -- 3.8.1 Text Editors for Linuxians -- 3.9 Further Reading -- 3.10 Complements, Problems, and Programs -- Chapter 4 Exploratory Data Analysis 9.3.1 Bayesian Sufficiency and the Principle -- 9.3.2 Bayesian Analysis and Likelihood Principle -- 9.3.3 Informative and Conjugate Prior -- 9.3.4 Non-informative Prior -- 9.4 Bayesian Estimation -- 9.4.1 Inference for Binomial Distribution -- 9.4.2 Inference for the Poisson Distribution -- 9.4.3 Inference for Uniform Distribution -- 9.4.4 Inference for Exponential Distribution -- 9.4.5 Inference for Normal Distributions -- 9.5 The Credible Intervals -- 9.6 Bayes Factors for Testing Problems -- 9.7 Further Reading -- 9.8 Complements, Problems, and Programs -- Part III Stochastic Processes and Monte Carlo -- Chapter 10 Stochastic Processes -- 10.1 Introduction -- 10.2 Kolmogorov's Consistency Theorem -- 10.3 Markov Chains -- 10.3.1 The m-Step TPM -- 10.3.2 Classification of States -- 10.3.3 Canonical Decomposition of an Absorbing Markov Chain -- 10.3.4 Stationary Distribution and Mean First Passage Time of an Ergodic Markov Chain -- 10.3.5 Time Reversible Markov Chain -- 10.4 Application of Markov Chains in Computational Statistics -- 10.4.1 The Metropolis-Hastings Algorithm -- 10.4.2 Gibbs Sampler -- 10.4.3 Illustrative Examples -- 10.5 Further Reading -- 10.6 Complements, Problems, and Programs -- Chapter 11 Monte Carlo Computations -- 11.1 Introduction -- 11.2 Generating the (Pseudo-) Random Numbers -- 11.2.1 Useful Random Generators -- 11.2.2 Probability Through Simulation -- 11.3 Simulation from Probability Distributions and Some Limit Theorems -- 11.3.1 Simulation from Discrete Distributions -- 11.3.2 Simulation from Continuous Distributions -- 11.3.3 Understanding Limit Theorems through Simulation -- 11.3.4 Understanding The Central Limit Theorem -- 11.4 Monte Carlo Integration -- 11.5 The Accept-Reject Technique -- 11.6 Application to Bayesian Inference -- 11.7 Further Reading -- 11.8 Complements, Problems, and Programs 7.5.2 The Fisher Information -- 7.6 Point Estimation -- 7.6.1 Maximum Likelihood Estimation -- 7.6.2 Method of Moments Estimator -- 7.7 Comparison of Estimators -- 7.7.1 Unbiased Estimators -- 7.7.2 Improving Unbiased Estimators -- 7.8 Confidence Intervals -- 7.9 Testing Statistical Hypotheses-The Preliminaries -- 7.10 The Neyman-Pearson Lemma -- 7.11 Uniformly Most Powerful Tests -- 7.12 Uniformly Most Powerful Unbiased Tests -- 7.12.1 Tests for the Means: One- and Two-Sample t-Test -- 7.13 Likelihood Ratio Tests -- 7.13.1 Normal Distribution: One-Sample Problems -- 7.13.2 Normal Distribution: Two-Sample Problem for the Mean -- 7.14 Behrens-Fisher Problem -- 7.15 Multiple Comparison Tests -- 7.15.1 Bonferroni's Method -- 7.15.2 Holm's Method -- 7.16 The EM Algorithm* -- 7.16.1 Introduction -- 7.16.2 The Algorithm -- 7.16.3 Introductory Applications -- 7.17 Further Reading -- 7.17.1 Early Classics -- 7.17.2 Texts from the Last 30 Years -- 7.18 Complements, Problems, and Programs -- Chapter 8 Nonparametric Inference -- 8.1 Introduction -- 8.2 Empirical Distribution Function and Its Applications -- 8.2.1 Statistical Functionals -- 8.3 The Jackknife and Bootstrap Methods -- 8.3.1 The Jackknife -- 8.3.2 The Bootstrap -- 8.3.3 Bootstrapping Simple Linear Model* -- 8.4 Non-parametric Smoothing -- 8.4.1 Histogram Smoothing -- 8.4.2 Kernel Smoothing -- 8.4.3 Nonparametric Regression Models* -- 8.5 Non-parametric Tests -- 8.5.1 The Wilcoxon Signed-Ranks Test -- 8.5.2 The Mann-Whitney test -- 8.5.3 The Siegel-Tukey Test -- 8.5.4 The Wald-Wolfowitz Run Test -- 8.5.5 The Kolmogorov-Smirnov Test -- 8.5.6 Kruskal-Wallis Test* -- 8.6 Further Reading -- 8.7 Complements, Problems, and Programs -- Chapter 9 Bayesian Inference -- 9.1 Introduction -- 9.2 Bayesian Probabilities -- 9.3 The Bayesian Paradigm for Statistical Inference Part IV Linear Models |
| Title | Course in Statistics with R |
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