Book Description 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 Show and hide more
Table of Contents
Cover Title Page Copyright Dedication 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 1.5 http://cran.r-project.org 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 2.3 Some Basic R Functions 2.4 Vectors and Matrices in R 2.5 Data Entering and Reading from 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 3.9 Further Reading 3.10 Complements, Problems, and Programs Chapter 4: Exploratory Data Analysis 4.1 Introduction: The Tukey's School of Statistics 4.2 Essential Summaries of EDA 4.3 Graphical Techniques in EDA 4.4 Quantitative Techniques in EDA 4.5 Exploratory Regression Models 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 5.4 Probability: A Definition 5.5 Conditional Probability and Independence 5.6 Bayes Formula 5.7 Random Variables, Expectations, and Moments 5.8 Distribution Function, Characteristic Function, and Moment Generation Function 5.9 Inequalities 5.10 Convergence of Random Variables 5.11 The Law of Large Numbers 5.12 The Central Limit Theorem 5.13 Further Reading 5.14 Complements, Problems, and Programs Chapter 6: Probability and Sampling Distributions 6.1 Introduction 6.2 Discrete Univariate Distributions 6.3 Continuous Univariate Distributions 6.4 Multivariate Probability Distributions 6.5 Populations and Samples 6.6 Sampling from the Normal Distributions 6.7 Some Finer Aspects of Sampling Distributions 6.8 Multivariate Sampling Distributions 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 7.3 Loss Functions 7.4 Data Reduction 7.5 Likelihood and Information 7.6 Point Estimation 7.7 Comparison of 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 7.13 Likelihood Ratio Tests 7.14 Behrens-Fisher Problem 7.15 Multiple Comparison Tests 7.16 The EM Algorithm* 7.17 Further Reading 7.18 Complements, Problems, and Programs Chapter 8: Nonparametric Inference 8.1 Introduction 8.2 Empirical Distribution Function and Its Applications 8.3 The Jackknife and Bootstrap Methods 8.4 Non-parametric Smoothing 8.5 Non-parametric Tests 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 9.4 Bayesian Estimation 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 10.4 Application of Markov Chains in Computational Statistics 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 11.3 Simulation from Probability Distributions and Some Limit Theorems 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 Part IV: Linear Models Chapter 12: Linear Regression Models 12.1 Introduction 12.2 Simple Linear Regression Model 12.3 The Anscombe Warnings and Regression Abuse 12.4 Multiple Linear Regression Model 12.5 Model Diagnostics for the Multiple Regression Model 12.6 Multicollinearity 12.7 Data Transformations 12.8 Model Selection 12.9 Further Reading 12.10 Complements, Problems, and Programs Chapter 13: Experimental Designs 13.1 Introduction 13.2 Principles of Experimental Design 13.3 Completely Randomized Designs 13.4 Block Designs 13.5 Factorial Designs 13.6 Further Reading 13.7 Complements, Problems, and Programs Chapter 14: Multivariate Statistical Analysis - I 14.1 Introduction 14.2 Graphical Plots for Multivariate Data 14.3 Definitions, Notations, and Summary Statistics for Multivariate Data 14.4 Testing for Mean Vectors : One Sample 14.5 Testing for Mean Vectors : Two-Samples 14.6 Multivariate Analysis of Variance 14.7 Testing for Variance-Covariance Matrix: One Sample 14.8 Testing for Variance-Covariance Matrix: -Samples 14.9 Testing for Independence of Sub-vectors 14.10 Further Reading 14.11 Complements, Problems, and Programs Chapter 15: Multivariate Statistical Analysis - II 15.1 Introduction 15.2 Classification and Discriminant Analysis 15.3 Canonical Correlations 15.4 Principal Component Analysis – Theory and Illustration 15.5 Applications of Principal Component Analysis 15.6 Factor Analysis 15.7 Further Reading 15.8 Complements, Problems, and Programs Chapter 16: Categorical Data Analysis 16.1 Introduction 16.2 Graphical Methods for CDA 16.3 The Odds Ratio 16.4 The Simpson's Paradox 16.5 The Binomial, Multinomial, and Poisson Models 16.6 The Problem of Overdispersion 16.7 The - Tests of Independence 16.8 Further Reading 16.9 Complements, Problems, and Programs Chapter 17: Generalized Linear Models 17.1 Introduction 17.2 Regression Problems in Count/Discrete Data 17.3 Exponential Family and the GLM 17.4 The Logistic Regression Model 17.5 Inference for the Logistic Regression Model 17.6 Model Selection in Logistic Regression Models 17.7 Probit Regression 17.8 Poisson Regression Model 17.9 Further Reading 17.10 Complements, Problems, and Programs Appendix A: Open Source Software–An Epilogue Appendix B: The Statistical Tables Bibliography Author Index Subject Index R Codes End User License Agreement
