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
Table of contents
- Cover
- Title Page
- List of Figures
- List of Tables
- Preface
- Acknowledgments
-
Part I: The Preliminaries
- Chapter 1: Why R?
- Chapter 2: The R Basics
-
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
-
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
- Chapter 9: Bayesian Inference
-
Chapter 5: Probability Theory
- Part III: Stochastic Processes and Monte Carlo
-
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
-
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
- Chapter 16: Categorical Data Analysis
-
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
-
Chapter 12: Linear Regression Models
- Appendix A: Open Source Software–An Epilogue
- Appendix B: The Statistical Tables
- Bibliography
- End User License Agreement
Product information
- Title: A Course in Statistics with R
- Author(s):
- Release date: May 2016
- Publisher(s): Wiley
- ISBN: 9781119152729
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