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Part I: The Preliminaries
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Part I: The Preliminaries
by B. G. Manjunath, Suresh Ramaiah, Prabhanjan N. Tattar
A Course in Statistics with R
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
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The Preliminaries
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