# A Course in Statistics with R

ISBN: 9788126578252

692 pages

## Description

This book will allow readers to seamlessly follow the theory and application of statistical methods with the aid of the popular and freely available R software package. The book shows that mathematical concepts can be richly illustrated through the use of a software in general, and R in particular. The coverage begins with R basics and visualizing techniques of exploratory data analysis. Concepts ranging from intuitive and counter-intuitive probability problems to central limit theorems are illustrated through R programs and diagrams. A similar wide coverage of the topics of statistical inference, nonparametrics, and Bayes theory is developed and many nuances of the paradigms are reflected through the software.

List of Figures

List of Tables

Preface

Acknowledgments

Part I The Preliminaries

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

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

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

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

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

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

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

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

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

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

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

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

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

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

14.8 Testing for Variance-Covariance Matrix: k-Samples

14.9 Testing for Independence of Sub-vectors

14.10 Further Reading

14.11 Complements, Problems, and Programs

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

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 ðœ’2- Tests of Independence

16.8 Further Reading

16.9 Complements, Problems, and Programs

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